HMMT 2005 G4

Let $X Y Z$ be a triangle with $\angle X=60^{\circ}$ and $\angle Y=45^{\circ}$. A circle with center $P$ passes through points $A$ and $B$ on side $X Y, C$ and $D$ on side $Y Z$, and $E$ and $F$ on side $Z X$. Suppose $A B=C D=E F$. Find $\angle X P Y$ in degrees.