Solve for φ (complex solution)
\phi =-\frac{i\ln(\frac{i\left(\sqrt{r^{2}-9}+r\right)}{3})}{3}+\frac{2\pi n_{1}}{3}\text{, }n_{1}\in \mathrm{Z}
\phi =-\frac{i\ln(\frac{-i\sqrt{r^{2}-9}+ir}{3})}{3}+\frac{2\pi n_{2}}{3}\text{, }n_{2}\in \mathrm{Z}
Solve for r
r=3\sin(3\phi )
Solve for φ
\phi =\frac{\arcsin(\frac{r}{3})+2\pi n_{1}}{3}\text{, }n_{1}\in \mathrm{Z}
\phi =\frac{-\arcsin(\frac{r}{3})+2\pi n_{2}+\pi }{3}\text{, }n_{2}\in \mathrm{Z}\text{, }|r|\leq 3
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