Let $\a_T$ and $\a_Z$, respectively, be the angles of $X$ and $C$ for $T$ and $Z$, respectively. Prove that
$$
\sin(\a_Z/2)=\frac{\sin(\a_T/2)}{\b\sqrt{1-ev}}
$$
In this case the factor of contraction also depends on the direction of $X$!
Again, we have $-\la X,T\ra=-\la C,T\ra=1$ and $-\la X,Z\ra=\b(1-ev)$, $-\la C,Z\ra=\b$; by \eqref{pereq1} we thus obtain the result.