Geometry Ratio

In $ABC$ , let $I$ be the center of the inscribed circle and let the bisector of angle $ACB$ intersect line $AB$ at $C$ . The line through $C$ and $I$ intersect the circumscribed circle of triangle $ABC$ at the two points $C$ and $D$ . If angle I=2 and angle D=3, then $IC=\frac{p}{q}$ , where $p$ and $q$ are coprime positive integers. Find $p + q$ .