MathNet 2013 Question 86

Let $A B C D E F$ be a convex hexagon with $A B = D E$, $B C = E F$, $C D = F A$, and $\angle A - \angle D = \angle C - \angle F = \angle E - \angle B$. Prove that the diagonals $A D$, $B E$, and $C F$ are concurrent.