Solve for R
\left\{\begin{matrix}R=r\left(\frac{1}{\sin(\theta )}+1\right)\text{, }&r\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\\R\neq 0\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\text{ and }r=0\end{matrix}\right.
Solve for r
\left\{\begin{matrix}r=\frac{R\sin(\theta )}{\sin(\theta )+1}\text{, }&R\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}+\frac{3\pi }{2}\\r\neq 0\text{, }&R=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}+\frac{3\pi }{2}\end{matrix}\right.
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