Let $ABC$ be an obtuse triangle with circumcenter $O$ such that $\angle ABC = 15^o$ and $\angle  BAC > 90^o$. Suppose that $AO$ meets $BC$ at $D$, and that $OD^2 + OC \cdot DC = OC^2$. Find $\angle  C$.

Let's think step by step and output the final answer within \boxed{}.
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