Triangle Problem

Geometry Level 4

In triangle ABC ABC , cosA:cosB:cosC=2:9:12 \cos A : \cos B : \cos C = 2 : 9 : 12 .

If sinA:sinB:sinC=p:q:r \sin A : \sin B : \sin C = p : q : r , where p p , q q and r r are coprime positive integers, find pqr(p+q+r) pqr-(p+q+r) .

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