Medals Are For Stars

Geometry Level 3

A medal is formed by incsribing a four-pointed star in a diamond of side 1, such that the angle between the points is \(120^{\circ}\) as shown.

If the area of the circle inscribed in the star is \(\dfrac{a-\sqrt3}{b} \pi\) for integers \(a\) and \(b\), find \(ab\).

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