What order is the pole at $z=0$?
$$\int\frac{\sin(3z)-3\sin(z)}{\sin(z)(\sin(z)-3)} dz$$
And do I calculate this this way:
$$\frac{1}{(n-1)!} \lim_{z\to 0} \frac{d^{n-1}}{dz^{n-1}} f(z)$$
P.S. I need to calculate residue at 0
2026-03-28 15:26:58.1774711618
what order is the pole at 0?
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HINT: Write the denominator and numerator as a power series, and simplify things. Then, check the least exponent of $z$ in the denominator: that will be the order of the pole. If, however, the least exponent is $0$, the function has a removable singularity.