ELMO 2012 Problem 5

Let $ABC$ be an acute triangle with $AB<AC$ , and let $D$ and $E$ be points on side $BC$ such that $BD=CE$ and $D$ lies between $B$ and $E$ . Suppose there exists a point $P$ inside $ABC$ such that $PD\parallel AE$ and $\angle PAB=\angle EAC$ . Prove that $\angle PBA=\angle PCA$ .

Calvin Deng.