A circle with a radius of 2 has a chord \(AB\) of 2. A square with a side \(AB\) is constructed, leaving the two other vertices outside the circle. If the total area of the figure can be expressed as \(\frac{a\pi}{b}+\sqrt{c}+d\), where a and b are relatively prime, what is \(a+b+c+d\)?

**Note: \(A\) is not equal to \(a\), and \(B\) is not equal to \(b\)**

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