IR-TST 2008 Problem 10

In the triangle $ABC$ , $\angle B$ is greater than $\angle C$ . $T$ is the midpoint of the arc $BAC$ from the circumcircle of $ABC$ and $I$ is the incenter of $ABC$ . $E$ is a point such that $\angle AEI=90^\circ$ and $AE\parallel BC$ . $TE$ intersects the circumcircle of $ABC$ for the second time in $P$ . If $\angle B=\angle IPB$ , find the angle $\angle A$ .