MEMO 2008 T3

Let $ABC$ be an acute-angled triangle. Let $E$ be a point such $E$ and $B$ are on distinct sides of the line $AC,$ and $D$ is an interior point of segment $AE.$ We have $\angle ADB = \angle CDE,$ $\angle BAD = \angle ECD,$ and $\angle ACB = \angle EBA.$ Prove that $B, C$ and $E$ lie on the same line.