US-TST 2002 Problem 1

Let $ABC$ be a triangle, and $A$ , $B$ , $C$ its angles. Prove that $$\sin\frac{3A}{2}+\sin\frac{3B}{2}+\sin\frac{3C}{2}\leq \cos\frac{A-B}{2}+\cos\frac{B-C}{2}+\cos\frac{C-A}{2}.$$