Question 199
Let $a, b, c$ be real numbers in the interval $(0, \frac{\pi}{2})$. Prove that
$$
\frac{\sin a \sin(a-b) \sin(a-c)}{\sin(b+c)} + \frac{\sin b \sin(b-c) \sin(b-a)}{\sin(c+a)} + \frac{\sin c \sin(c-a) \sin(c-b)}{\sin(a+b)} \ge 0.
$$
$$
\frac{\sin a \sin(a-b) \sin(a-c)}{\sin(b+c)} + \frac{\sin b \sin(b-c) \sin(b-a)}{\sin(c+a)} + \frac{\sin c \sin(c-a) \sin(c-b)}{\sin(a+b)} \ge 0.
$$