Question 177
Suppose $A$, $B$, and $C$ are the angles in an acute-angled triangle. Prove that
$$
\frac{\sin 2A + \sin 2B + \sin 2C}{\cos A + \cos B + \cos C} \le \sqrt{3}.
$$
$$
\frac{\sin 2A + \sin 2B + \sin 2C}{\cos A + \cos B + \cos C} \le \sqrt{3}.
$$