Solve (text{cosee}Q-cotθ)^2=1-cosθ/1+cosθ

$$( \text { cosee } Q - \cot \theta ) ^ { 2 } = \frac { 1 - \cos \theta } { 1 + \cos \theta }$$

Solve for Q (complex solution)

$$Q=\frac{\left(\cos(\theta )+1\right)^{-\frac{1}{2}}\left(\sqrt{\cos(\theta )+1}\cos(\theta )-i\sqrt{\cos(\theta )-1}\sin(\theta )\right)}{\cos(e^{2})\sin(\theta )}$$

$$Q=\frac{\left(\cos(\theta )+1\right)^{-\frac{1}{2}}\left(\sqrt{\cos(\theta )+1}\cos(\theta )+i\sqrt{\cos(\theta )-1}\sin(\theta )\right)}{\cos(e^{2})\sin(\theta )}\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}$$