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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 ab+cd,a\sqrt{b}+\dfrac{c}{d}, where a,b,ca,b,c and dd are integers with bb square-free and c,dc,d coprime.

Find ab+cdab+cd.

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