I need to find the Taylor expansion at $z=0$ of $f(z)=\ln\frac{1-z^3}{1+z^3}$
I had two approaches:
The first,
$f(z)=\ln\frac{1-z^3}{1+z^3} = \ln(1-z^3) - \ln(1+z^3)$ but I realized that this is not true in the complex case.
The second,
$f(z)=\ln\frac{1-z^3}{1+z^3} = \ln(1+\frac{-2z^3}{1+z^3})$ and continue with the "normal" taylor expansion but this doesn't seen to get me to the solution.
I'd be happy for an idea.