$ \sin\theta_1\cos\theta_2 + \sin\theta_2\cos\theta_3 + \ldots + \sin\theta_{2007}\cos\theta_{2008} + \sin\theta_{2008}\cos\theta_1\leq\frac{1}{2} \sum (\sin^2\theta_i+\cos^2\theta_{i+1}) = 1004$ Equality holds when $ \theta_i$ is constant

brianchung11 wrote: $ \sin\theta_1\cos\theta_2 + \sin\theta_2\cos\theta_3 + \ldots + \sin\theta_{2007}\cos\theta_{2008} + \sin\theta_{2008}\cos\theta_1\leq\frac {1}{2} \sum (\sin^2\theta_i + \cos^2\theta_{i + 1}) = 1004$ Equality holds when $ \theta_i$ is constant The constant is $ \frac{\pi}{4}$