Question regarding covert multiple poles when calculating residues
Hey guys, I was told by my lecturer, that if we come across a covert multiple pole when trying to find the residue of a complex function, we have to either make it into a simpler form (i.e. covert simple or overt multiple forms) or find the coefficient of z^-1 by finding its Laurent expansion about its poles. This is all fine and good, but when I came across something like 1/sin^2(z), I had a bit of a problem finding its residues through simplification of its poles. I know that this function has a double covert pole at z= k(pi), but I don't really like finding Laurent expansions as they are quite involved when compared to normal residue finding methods. I was wondering if this would be possible:
Make sin^2(z) = (1/2i)e^2iz - (1/2i)e^-2iz, and then find the residues using simple covert methods. Would this be regarded as a covert simple form or is it still in its double covert form?