Geometry Level 5

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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