Let $X \left( s\right)$ be a stationary process with finite second moment and $E \left( X \left( s \right) \right) = 0$. Suppose $$Z \left( s \right) = \frac{1}{2} \left[ 1 + \frac{X \left( s\right) X \left( s+h \right)}{\left| X \left( s\right) X \left( s+h \right)\right|} \right].$$
Show that $$E \left( Z \left( s \right) \right) = \frac{1}{\pi}cos^{-1} \left( -R_X \left( h \right) \right)$$
where $R_X \left( h \right)$ is the correlation function of $X \left( s \right)$.
This is not homework. I don't know where to start.