Show that

$\displaystyle \frac{1}{2 \pi} \int_{-\pi}^{\pi} \frac{1}{1-2r\cos \theta +r^2} d \theta = 1, 0 \leq r < 1$.

Right now, I don't see how to show this. I do see that the integrand is an even function if that helps at all. Also, since this is not from $\displaystyle -\infty$ to $\displaystyle \infty$, I do not know the method to proceed. I need a few hints on how to start.