In \(\Delta{ABC}\),

\[\overline{AB}^2+\overline{BC}^2+\overline{AC}^2 = \cos{A}\sin{B}\sin{C}+\sin{A}\cos{B}\sin{C}+\sin{A}\sin{B}\cos{C}.\]

If the area of the circumcircle of \(\Delta{ABC}\) can be represented as \(\frac{a\pi}{b}\), where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b?\)

\(\)

**Note:** This problem is posed by Kshitij J.

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