ISL 2006 G2

Let $A B C D$ be a trapezoid with parallel sides $A B>C D$. Points $K$ and $L$ lie on the line segments $A B$ and $C D$, respectively, so that $A K / K B=D L / L C$. Suppose that there are points $P$ and $Q$ on the line segment $K L$ satisfying $$\angle A P B=\angle B C D \text { and } \angle C Q D=\angle A B C \text {. }$$ Prove that the points $P, Q, B$ and $C$ are concyclic. (Ukraine)