IR-TST 2015 Problem 18

$AH$ is the altitude of triangle $ABC$ and $H^\prime$ is the reflection of $H$ trough the midpoint of $BC$ . If the tangent lines to the circumcircle of $ABC$ at $B$ and $C$ , intersect each other at $X$ and the perpendicular line to $XH^\prime$ at $H^\prime$ , intersects $AB$ and $AC$ at $Y$ and $Z$ respectively, prove that $\angle ZXC=\angle YXB$ .