Triangle ABC

Geometry Level 4

In triangle ABCABC, let aa, bb and cc be the sides corresponding to A\angle A, B\angle B and C\angle C, respectively. The side lengths of ABCABC satisfy the following two equations: a4b+4c=0a - 4b + 4c = 0 and a+2b3c=0a + 2b - 3c = 0. If sinAsinB+sinC=mn\frac{\sin \angle A}{\sin \angle B + \sin \angle C} = \frac{m}{n}, where mm and nn are coprime positive integers, what is the value of m+nm+n?

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