UZ-MO 2014 Problem 4

A circle passes through the points $A,C$ of triangle $ABC$ intersects with the sides $AB,BC$ at points $D,E$ respectively. Let $\frac{BD}{CE}=\frac{3}{2}$ , $BE=4$ , $AD=5$ and $AC=2\sqrt{7}$ . Find the angle $\angle BDC$ .