Use residue theorem to establish the integration formula: $$\int_0^{2\pi} \frac{\cos^2(3\theta)}{5-4\cos(2\theta)}d\theta = \frac{3\pi}{8}$$

Hi, so I'm stuck on this question. I've gotten up to computing the residues as being $z_{+/-} = 1/\sqrt2$ and $z = 0$ though I'm not sure how to go from here.

EDIT: Okay I've gotten to the point of knowing that the value of the integral is equal to the sum of the residues at each singularity, though I am having difficulty with computing the residue at $z = 0$. That is the only issue I'm having left.


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