$\int_{0}^{\pi} \frac{dx}{(2 - \cos{x})^2}$ [duplicate]

For $a > 1$ we define the integral with the parameter

$$F(a) = \int_{0}^{\pi} \frac{dx}{a - \cos{x}}$$

I was able to find $F(a) = \frac{\pi}{\sqrt{a^2 - 1}}$. Any idea, how can I from here evaluate the following integral:

$$\int_{0}^{\pi} \frac{dx}{(2 - \cos{x})^2}.$$