ILL 1992 Problem 4

Let $p, q$ , and $r$ be the angles of a triangle, and let $a = \sin2p, b = \sin2q$ , and $c = \sin2r$ . If $s = \frac{(a + b + c)}2$ , show that $$s(s - a)(s - b)(s -c) \geq 0.$$ When does equality hold?