Solve (x+xxi)tau<(x-tau)varepsilon

$$( x + x \xi ) \tau < ( x - \tau ) \varepsilon$$

Solve for x

$$\left\{\begin{matrix}x<-\frac{2\pi \epsilon }{2\pi +2\pi \xi -\epsilon }\text{, }&\xi >\frac{\epsilon }{2\pi }-1\\x\in \mathrm{R}\text{, }&\epsilon <0\text{ and }\xi =\frac{\epsilon }{2\pi }-1\\x>-\frac{2\pi \epsilon }{2\pi +2\pi \xi -\epsilon }\text{, }&\xi <\frac{\epsilon }{2\pi }-1\end{matrix}\right.$$

Solve for ξ

$$\left\{\begin{matrix}\xi <\frac{x\epsilon -2\pi x-2\pi \epsilon }{2\pi x}\text{, }&x>0\\\xi \in \mathrm{R}\text{, }&\left(x>-\frac{2\pi \epsilon }{2\pi -\epsilon }\text{ and }\epsilon >2\pi \right)\text{ or }\left(x<-\frac{2\pi \epsilon }{2\pi -\epsilon }\text{ and }\epsilon <2\pi \right)\\\xi >\frac{x\epsilon -2\pi x-2\pi \epsilon }{2\pi x}\text{, }&x<0\end{matrix}\right.$$