Question 176
Suppose $x$, $y$, $z$ are positive numbers that sum to $\pi$. Prove that
$$
\frac{\sin 2x + \sin 2y + \sin 2z}{\sin x + \sin y + \sin z} \le 1,
$$
with equality iff $x = y = z = \pi/3$.
$$
\frac{\sin 2x + \sin 2y + \sin 2z}{\sin x + \sin y + \sin z} \le 1,
$$
with equality iff $x = y = z = \pi/3$.