IR-TST 2009 Problem 10

Let $ABC$ be a triangle and $AB\ne AC$ . $D$ is a point on $BC$ such that $BA = BD$ and $B$ is between $C$ and $D$ . Let $I_{c}$ be center of the circle which touches $AB$ and the extensions of $AC$ and $BC$ . $CI_{c}$ intersect the circumcircle of $ABC$ again at $T$ . If $\angle TDI_{c} = \frac {\angle B + \angle C}{4}$ then find $\angle A$