Question 41
Let $a$, $b$, $c$ be the sides and $\alpha$, $\beta$, $\gamma$ the corresponding angles of the triangle $ABC$ with area $P$. Prove that the following equality holds:
$$
a^2(\sin 2\beta + \sin 2\gamma) + b^2(\sin 2\gamma + \sin 2\alpha) + c^2(\sin 2\alpha + \sin 2\beta) = 12P.
$$
$$
a^2(\sin 2\beta + \sin 2\gamma) + b^2(\sin 2\gamma + \sin 2\alpha) + c^2(\sin 2\alpha + \sin 2\beta) = 12P.
$$