Question 113
Let the medians of the triangle $A B C$ meet at $M$. Let $D$ and $E$ be different points on the line $B C$ such that $D C = C E = A B$, and let $P$ and $Q$ be points on the segments $B D$ and $B E$, respectively, such that $2 B P = P D$ and $2 B Q = Q E$. Determine $\angle P M Q$.