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A medal is formed by incsribing a four-pointed star in a diamond of side 1, such that the angle between the points is 120∘120^{\circ}120∘ as shown.
If the area of the circle inscribed in the star is a−3bπ\dfrac{a-\sqrt3}{b} \piba−3π for integers aaa and bbb, find ababab.
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