A nice Geometry Problem

The following problem is an example of how deceptive a seemingly simple geometry problem can be. Angle chasing is not going to lead anywhere.

Problem.

Let $\triangle ABC$ be isosceles with $AB=AC$ and $\angle BAC = 20^\circ$. Point $D$ is on side $AC$ such that $\angle DBC = 60^\circ$. Point $E$ is on side $AB$ such that $\angle ECB = 50^\circ$. Find, with proof, the measure of $\angle EDB$.

Source: Mathematical Gazette 1922