Let $I$ be the incenter of $\triangle ABC$ with $AB>AC$. Let $\Gamma$ be the circle with diameter $AI$. The circumcircle of $\triangle ABC$ intersects $\Gamma$ at points $A,D$, with point $D$ lying on $\overarc{AC}$ (not containing $B$). Let the line passing through $A$ and parallel to $BC$ intersect $\Gamma$ at points $A,E$. If $DI$ is the angle bisector of $\angle CDE$, and $\angle ABC = 33^{\circ}$, find the value of $\angle BAC$.