A problem by Fahim Shahriar Shakkhor

Level pending

\(\triangle ABC\) is inscribed in a circle with radius \(\sqrt{\frac{2}{3}}\). Given that \(\angle ABC = 45^\circ\) & \(\angle ACB = 75^\circ\). The perimeter of the triangle can be written as \(\sqrt{a} + \sqrt{b} + c \) ; where \(a,b,c\) are positive integers. Find \(a+b+c\).

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