begin{align}
cos sum_n theta_n
& = sum_{text{even } k} (-1)^{k/2}
sum_{(A,:,|A|=k)} prod_{nin A} sintheta_n prod_{nnotin A} costheta_n \
sin sum_n theta_n
& = sum_{text{odd } k} (-1)^{(k-1)/2}
sum_{(A,:,|A|=k)} prod_{nin A} sintheta_n prod_{nnotin A} costheta_n
end{align}

begin{align}
cos sum_n theta_n
& = sum_{text{even } k} (-1)^{k/2}
& sum_{(A,:,|A|=k)} prod_{nin A} sintheta_n prod_{nnotin A} costheta_n \
sin sum_n theta_n
& = sum_{text{odd } k} (-1)^{(k-1)/2}
& sum_{(A,:,|A|=k)} prod_{nin A} sintheta_n prod_{nnotin A} costheta_n
end{align}