Question 153
Let $\alpha$, $\beta$, and $\gamma$ be three angles of a triangle. Prove that
$$
\cos(\alpha) \cos(3\alpha) + \cos(\beta) \cos(3\beta) + \cos(\gamma) \cos(3\gamma) + \frac{7}{4} \ge 2 \cos(\alpha) \cos(\beta) \cos(\gamma).
$$
(Otgonbayar Uuye)
$$
\cos(\alpha) \cos(3\alpha) + \cos(\beta) \cos(3\beta) + \cos(\gamma) \cos(3\gamma) + \frac{7}{4} \ge 2 \cos(\alpha) \cos(\beta) \cos(\gamma).
$$
(Otgonbayar Uuye)