# Triangle Problem

Geometry Level 4

In triangle $$ABC$$, $$\cos A : \cos B : \cos C = 2 : 9 : 12.$$

If $$\sin A : \sin B : \sin C = p : q : r$$, where $$p$$, $$q$$ and $$r$$ are coprime positive integers, find the value of $$pqr-(p+q+r).$$

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