How can one estimate $(1/2)\int_{-\pi}^{\pi}|D_N|dx$,here DN is the Dirichlet kernel

Question

The Dirichlet Kernel $$D_N =\frac{\sin(N+1/2)x}{\sin x/2}$$ How to show this $$\frac{1}{2\pi}\int_{\pi}^{\pi}|D_N|dx=\frac{4}{\pi^2}\log N+O(1)$$