# Triangle ABC

Geometry Level 4

In triangle $ABC$, let $a$, $b$ and $c$ be the sides corresponding to $\angle A$, $\angle B$ and $\angle C$, respectively. The side lengths of $ABC$ satisfy the following two equations: $a - 4b + 4c = 0$ and $a + 2b - 3c = 0$. If $\frac{\sin \angle A}{\sin \angle B + \sin \angle C} = \frac{m}{n}$, where $m$ and $n$ are coprime positive integers, what is the value of $m+n$?

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