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I've been self-studying some complex variables and just started on residues. I'm looking at a problem where I've been asked to calculate the residue of:

$$f(z) = \frac{z}{1-\cos(z)}$$

at $z=0$. I'm not really sure how to find the Laurent series of this function, and I can't really apply Cauchy's integral formula either. So I would appreciate if anyone can get me started.

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