ZA-SAMO 2016 Problem 3

The inscribed circle of triangle $ABC$ , with centre $I$ , touches sides $BC$ , $CA$ and $AB$ at $D$ , $E$ and $F$ , respectively. Let $P$ be a point, on the same side of $FE$ as $A$ , for which $\angle PFE = \angle BCA$ and $\angle PEF = \angle ABC$ . Prove that $P$ , $I$ and $D$ lie on a straight line.