A concentric circle, (radius \(\dfrac{2}{\sqrt{3}}\)), and square, (side length \(2\)), have a region of overlap with an area of

\(\dfrac{a}{b} \sqrt{b} + \dfrac{a}{c} \pi\),

where \(a\) is coprime with both \(b\) and \(c\). Find \(a + b + c\).

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