Question 136
An acute-angled triangle $A B C$ is given. Let $E$ be a point such that $B$ and $E$ lie on different sides of the line $A C$, and let $D$ be an interior point of the segment $A E$. Suppose that $\angle A D B = \angle C D E$, $\angle B A D = \angle E C D$ and $\angle A C B = \angle E B A$. Prove that $B, C$ and $E$ are collinear.