How to Find Residues with g/h Rule and Differentiation

Find the residues of f(z) = pi^2cosec (pi z)/3z^2+1 .
We first of all find the poles by making 3z^2+1=0 , z= i/sqrt(3) or z= -i/sqrt(3).
Trig identity icosec(iz) equals csch(x)
As the function f(z) is an odd function we can see that the 2 residues are in fact the same .
The residue theorem is vital for finding things such as summing series , integrals etc .
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