In triangle $ABC$ $(b \geq c)$, point $E$ is the midpoint of shorter arc $BC$. If $D$ is the point such that $ED$ is the diameter of circumcircle $ABC$, prove that $\angle DEA = \frac{1}{2}(\beta-\gamma)$
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014
Tags: geometry, circumcircle