# Triangle ABC's Angles

Geometry Level pending

The angles in triangle $$ABC$$ satisfy $6 \sin \angle A = 3\sqrt{3} \sin \angle B = 2\sqrt{2} \sin \angle C.$ If $$\sin^2 \angle A = \frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b$$?

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