Let $\triangle ABC$ be a triangle, and $A$, $B$, $C$ its angles. Prove that:
\[ \sin\frac{3A}{2}+\sin\frac{3B}{2}+\sin\frac{3C}{2}\leq \cos\frac{A-B}{2}+\cos\frac{B-C}{2}+\cos\frac{C-A}{2}.\]
USA Team Selection Test 2002,P1
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