SE-SKOLORNAS 1997 Problem 2

Let $D$ be the point on side $AC$ of a triangle $ABC$ such that $BD$ bisects $\angle B$ , and $E$ be the point on side $AB$ such that $3\angle ACE = 2\angle BCE$ . Suppose that $BD$ and $CE$ intersect at a point $P$ with $ED = DC = CP$ . Determine the angles of the triangle.