I just wanted to find the principal part of
$ f(z) = \frac{1}{(1-z^3)^2} $
by calculating the negative coefficients of its Laurent series expansion applying
$ a_{n} = \frac{1}{2\pi i}\oint \frac{f(z)dz}{(z-z_0)^{n+1}}$
with the singularity at $ z_0 = 1$, but I got stuck quite at the beginning with a fourth order polynomial in z squared in the denominator etc. So I thought what I'm doing is probably wrong ...
Did I try the right approach after all, or is there a trick / much simpler / better way how to find the principle part in this case ?