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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