HK-PC 2009 Problem 1

Let $\alpha_1$, $\alpha_2$, $\ldots$, $\alpha_{2008}$ be real numbers. Find the maximum value of $$\sin\alpha_1\cos\alpha_2 + \sin\alpha_2\cos\alpha_3 + \cdots + \sin\alpha_{2007}\cos\alpha_{2008} + \sin\alpha_{2008}\cos\alpha_1$$