IMC 2011 — Keystage 3 (IWYMIC) — team Question 8

In triangle $ABC$, $BC=AC$ and $\angle BCA=90^\circ$. Points $D,E$ lie on $AC,AB$ respectively, with $AD=AE$ and $2CD=BE$. Let $P$ be the intersection of $BD$ and the bisector of $\angle CAB$. Find $\angle PCB$ in degrees.