Drawing Euler angle unit axis roations with LaTeX and TikZ

\documentclass[landscape]{article}

\usepackage{wasysym}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{pgfplots}
   % Workaround for making use of externalization possible
   % -> remove hardcoded pdflatex and replace by lualatex
   \usepgfplotslibrary{external}
       \tikzset{external/system call={lualatex \tikzexternalcheckshellescape%
        -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"}}

% Redefine rotation sequence for tikz3d-plot to z-y-x
\newcommand{\tdseteulerxyz}{
\renewcommand{\tdplotcalctransformrotmain}{%
%perform some trig for the Euler transformation
\tdplotsinandcos{\sinalpha}{\cosalpha}{\tdplotalpha}
\tdplotsinandcos{\sinbeta}{\cosbeta}{\tdplotbeta}
\tdplotsinandcos{\singamma}{\cosgamma}{\tdplotgamma}
%
\tdplotmult{\sasb}{\sinalpha}{\sinbeta}
\tdplotmult{\sasg}{\sinalpha}{\singamma}
\tdplotmult{\sasbsg}{\sasb}{\singamma}
%
\tdplotmult{\sacb}{\sinalpha}{\cosbeta}
\tdplotmult{\sacg}{\sinalpha}{\cosgamma}
\tdplotmult{\sasbcg}{\sasb}{\cosgamma}
%
\tdplotmult{\casb}{\cosalpha}{\sinbeta}
\tdplotmult{\cacb}{\cosalpha}{\cosbeta}
\tdplotmult{\cacg}{\cosalpha}{\cosgamma}
\tdplotmult{\casg}{\cosalpha}{\singamma}
%
\tdplotmult{\cbsg}{\cosbeta}{\singamma}
\tdplotmult{\cbcg}{\cosbeta}{\cosgamma}
%
\tdplotmult{\casbsg}{\casb}{\singamma}
\tdplotmult{\casbcg}{\casb}{\cosgamma}
%
%determine rotation matrix elements for Euler transformation
\pgfmathsetmacro{\raaeul}{\cacb}
\pgfmathsetmacro{\rabeul}{\casbsg - \sacg}
\pgfmathsetmacro{\raceul}{\sasg + \casbcg}
\pgfmathsetmacro{\rbaeul}{\sacb}
\pgfmathsetmacro{\rbbeul}{\sasbsg + \cacg}
\pgfmathsetmacro{\rbceul}{\sasbcg - \casg}
\pgfmathsetmacro{\rcaeul}{-\sinbeta}
\pgfmathsetmacro{\rcbeul}{\cbsg}
\pgfmathsetmacro{\rcceul}{\cbcg}
}
}

\tdseteulerxyz

\usepackage{siunitx}


%%%%%%%%% Z
\begin{document}
% Set the plot display orientation
% Syntax: \tdplotsetdisplay{\theta_d}{\phi_d}
\tdplotsetmaincoords{60}{140}

\pgfmathsetmacro{\zRot}{10}
\pgfmathsetmacro{\yRot}{10}
\pgfmathsetmacro{\xRot}{10}

% Start tikz picture, and use the tdplot_main_coords style to implement the display
% coordinate transformation provided by 3dplot.
\begin{tikzpicture}[scale=2,tdplot_main_coords]

% Set origin of main (body) coordinate system
\coordinate (O) at (0,0,0);

% Draw main coordinate system
\draw[red, ,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x_{\mathcal{I}}$};
\draw[red, ,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y_{\mathcal{I}}$};
\draw[red, ,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z_{\mathcal{I}}$,
    \textcolor{blue}{$z'$}};

% Intermediate frame 1
\tdplotsetrotatedcoords{\zRot}{0}{0}
\draw[thick,tdplot_rotated_coords,->, blue] (0,0,0) -- (1,0,0) node[anchor=north east]{$x'$};
\draw[thick,tdplot_rotated_coords,->, blue] (0,0,0) -- (0,1,0) node[anchor=west]{$y'$};
\draw[thick,tdplot_rotated_coords,->, blue] (0,0,0) -- (0,0,1) node[anchor=west]{};

\end{tikzpicture}
%%%%%%%%%%%%%%%%% Z-Y
\begin{tikzpicture}[scale=2,tdplot_main_coords,font=\small]
        thick,
% Set origin of main (body) coordinate system
\coordinate (O) at (0,0,0);

% Draw main coordinate system
\draw[red, ,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x_{\mathcal{I}}$};
\draw[red, ,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y_{\mathcal{I}}$};
\draw[red, ,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z_{\mathcal{I}}$};

% Intermediate frame 1
\tdplotsetrotatedcoords{\zRot}{0}{0}
\draw[tdplot_rotated_coords,->, blue] (0,0,0) -- (1,0,0) node[anchor=north east]{$x'$};
\draw[tdplot_rotated_coords,->, blue] (0,0,0) -- (0,1,0) node[anchor=west]{};
\draw[tdplot_rotated_coords,->, blue] (0,0,0) -- (0,0,1) node[anchor=west]{$z'$};

% Intermediate frame 2
\tdplotsetrotatedcoords{\zRot}{\yRot}{0}
\draw[thick,tdplot_rotated_coords,->, green] (0,0,0) -- (1,0,0)
node[anchor=north ]{$x''$};
\draw[thick,tdplot_rotated_coords,->, green] (0,0,0) -- (0,1,0)
node[anchor=west]{$y''$, \textcolor{blue}{$y'$}};
\draw[thick,tdplot_rotated_coords,->, green] (0,0,0) -- (0,0,1)
node[anchor=east]{$z''$};

\end{tikzpicture}
%%%%%%%%%%%%% Z-Y-X
\begin{tikzpicture}[scale=2.5,tdplot_main_coords]

% Set origin of main (body) coordinate system
\coordinate (O) at (0,0,0);

% Draw main coordinate system
\draw[red, ,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x_{\mathcal{I}}$};
\draw[red, ,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y_{\mathcal{I}}$};
\draw[red, ,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z_{\mathcal{I}}$};

% Intermediate frame 1
\tdplotsetrotatedcoords{\zRot}{0}{0}
\draw[tdplot_rotated_coords,->, blue] (0,0,0) -- (1,0,0) node[anchor=north east]{$x'$};
\draw[tdplot_rotated_coords,->, blue] (0,0,0) -- (0,1,0) node[anchor=west]{$y'$};
\draw[tdplot_rotated_coords,->, blue] (0,0,0) -- (0,0,1) node[anchor=west]{$z'$};

% Intermediate frame 2
\tdplotsetrotatedcoords{\zRot}{\yRot}{0}
\draw[,tdplot_rotated_coords,->, green] (0,0,0) -- (1,0,0) node[anchor=
north]{};
\draw[,tdplot_rotated_coords,->, green] (0,0,0) -- (0,1,0)
node[anchor=west]{$y''$};
\draw[,tdplot_rotated_coords,->, green] (0,0,0) -- (0,0,1)
node[anchor=south]{$z''$};

% Rotate to final frame
\tdplotsetrotatedcoords{\zRot}{\yRot}{\xRot}
\draw[thick,tdplot_rotated_coords,->, cyan] (0,0,0) -- (1,0,0)
node[anchor=west]{$x_{\mathcal{B}}$, \textcolor{green}{$x''$}};
\draw[thick,tdplot_rotated_coords,->, cyan] (0,0,0) -- (0,1,0) node[anchor=west]{$y_{\mathcal{B}}$};
\draw[thick,tdplot_rotated_coords,->, cyan] (0,0,0) -- (0,0,1) node[anchor=south]{$z_{\mathcal{B}}$};

\end{tikzpicture}

\end{document}