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Geometry Level 4

The figure shows a unit circle with a square and an equilateral triangle inscribed in it.

The square and equilateral triangle share a vertex.

The overlapping area of the square and triangle can be expressed as $a\sqrt{b}+\dfrac{c}{d},$ where $a,b,c$ and $d$ are integers with $b$ square-free and $c,d$ coprime.

Find $ab+cd$.

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