Laurent Expansion of Cotangent and Cosecant
Formula
$$ \cot z = {{1} \over {z}} - {{z} \over {3}} - {{z^{3}} \over {45}} - {{2 z^{5}} \over {945}} - \cdots \\ \csc z = {{1} \over {z}} + {{z} \over {6}} + {{7 z^{3}} \over {360}} + {{31 z^{5}} \over {15120}} + \cdots $$
Explanation
In complex analysis, to use the sum of series formula, one must be able to find the residue of a function multiplied by cotangent and cosecant. Of course, there are more elegant series forms that can be used even for higher-order terms, but this much is usually sufficient. It would be advisable to memorize the coefficients up to at least the third term, if only for exam preparation.