$$r = b \sin 2 \theta$$
$\left\{\begin{matrix}b=\frac{r}{\sin(2\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\\b\in \mathrm{C}\text{, }&r=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\end{matrix}\right.$
$\left\{\begin{matrix}b=\frac{r}{\sin(2\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\\b\in \mathrm{R}\text{, }&r=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\end{matrix}\right.$
$r=b\sin(2\theta )$