Slightly inflated square

Geometry Level 4

The figure above consists of 4 identical intersecting quadrants inside a square of side 4. The area of the shaded region can be expressed as \(\frac{a}{b}\pi+c-d\sqrt{e}\) for positive integers \(a,b,c,d\) with \(e\) with \(a\) and \(b\) are relatively coprime, and \(e\) is square free.

Evaluate the value of \(a+b+c+d+e\).

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