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 \( pqr-(p+q+r) \).

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