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## Homework Statement

Evaluate [tex]\int_{0}^{2\pi} \frac{d\theta}{1+\epsilon cos\theta}[/tex]

where [tex]\left|\epsilon\right|<1[/tex], by letting [tex]z=e^{i\theta}[/tex] and [tex]cos\theta = (z+z^{-1})/2[/tex] and choosing contour [tex]\left|z\right| = 1[/tex], a unit circle.

## Homework Equations

I know this has something to do with contour integration, but there are no poles as far as I'm aware and I'm used to going from [tex]dz[/tex] to [tex]d\theta[/tex] that I'm a bit confused here as to what to do.

## The Attempt at a Solution

I've gotten as far as subbing in the relevent replacement, but I'm lost otherwise. Residues don't apply here, right?