Kshitij's circumcircle

Geometry Level 4

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.