Challenging Geometry.

Let $ABC$ be a triangle with circumcircle $\Gamma$ and incentre $I$ . Let $M$ be the midpoint of side $BC$ . Denote by $D$ the foot of perpendicular from $I$ to side $BC$ . The line through $I$ perpendicular to $AI$ meets sides $AB$ and $AC$ at $F$ and $E$ respectively. Suppose the circumcircle of triangle $AEF$ intersects $\Gamma$ at a point $X$ other than $A$ .

Suppose $XD$ and $AM$ meet at $Z$ .

Let $S$ be the circumcentre of $\triangle ABC$ and $\angle XSA = { 60 }^{ o }$ . Find angle $XZA$ in degrees.