JBMO 2006 Problem 2

The triangle $ABC$ is isosceles with $AB=AC$ , and $\angle{BAC}<60^{\circ}$ . The points $D$ and $E$ are chosen on the side $AC$ such that, $EB=ED$ , and $\angle{ABD}\equiv\angle{CBE}$ . Denote by $O$ the intersection point between the internal bisectors of the angles $\angle{BDC}$ and $\angle{ACB}$ . Compute $\angle{COD}$ .