Hard limit of sine function How can I compute this limit : $$\lim_{n \to \infty } {1 \over n}\sum\limits_{k = 1}^n {\left\lvert \sin k\right\rvert} $$
Thank you.

Hint: $|\sin k|=\sin (k \bmod \pi)$  The values of $k \bmod \pi$ will bounce around in the interval $[0,\pi)$ so you are asked for the average value of $\sin x$ over this interval.  What integral can you do to get this?
