xchoice = [0, 1, Cos[[Alpha] x], Sin[[Alpha] x]]
ychoice = [0, 1, Cos[[Beta] y], Sin[[Beta] y], Cos[2 [Beta] y],
Sin[2 [Beta] y]]

zchoice = [0, 1, Cos[[Gamma] z], Sin[[Gamma] z]]

{Cos[2 y [Beta]] Sin[z [Gamma]], 0, 0}

{0, Sin[x [Alpha]] Sin[2 y [Beta]] Sin[z [Gamma]], Cos[2 y [Beta]] Cos[z [Gamma]] Sin[x [Alpha]]}