OIM 2012 Problem 1

Let $ABCD$ be a rectangle. Construct equilateral triangles $BCX$ and $DCY$ , in such a way that both of these triangles share some of their interior points with some interior points of the rectangle. Line $AX$ intersects line $CD$ on $P$ , and line $AY$ intersects line $BC$ on $Q$ . Prove that triangle $APQ$ is equilateral.