Suppose $Z=\b(T+vE)$, $X=T+fF+e_1E$, $Y=T+gG+e_2E$ such that $F,G\perp[E,T]$. Determine conditions that guarentee that the angle of $X$ and $Y$ for $Z$ and $T$ coincide.
$\a_Z=\a_T$ iff $\la X,Z\ra\la Y,Z\ra=\la X,T\ra\la Y,T\ra$, which holds if and only if: $(1-e_1v)(1-e_2v)=1-v^2$.