Residue of a Function Not at the Pole

Question

How do we calculate the residue of $$f\left(z\right) = \frac{z\sin\left(z\right)}{\left(z-\pi\right)^{3}}$$ at $z=3$, using the equation $$R\left(z_{0}\right) = \lim_{z\to z_{0}}\left[\frac{1}{\left(m - 1\right)!}\frac{d^{m-1}}{dz^{m-1}}\left[\left(z-z_{0}\right)^{m}f\left(z\right)\right]\right]$$

Answer 1

Easy: the residue is zero as the function is analytic at $\;z=3\;$ and in some neighborhood of it.

If you insist in using limits then you need to do that with the function $\;z-3\;$ , as the $\;m\;$ you get there is zero...