# Hello trig, my old friend

Geometry Level 4

If the maximum of $$S=\sqrt{\sin \alpha \sin \beta \cos \gamma}+\sqrt{\sin \beta \sin \gamma \cos \alpha}+\sqrt{\sin \gamma \sin \alpha \cos \beta}$$ can be represented as $$\frac{a\sqrt{b}}{c}$$, where $$\alpha$$, $$\beta$$ and $$\gamma$$ are angles of an acute-angle triangle, $$a$$ and $$c$$ irreducible and $$b$$ square-free , compute $$a+b+c$$.

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