gamma=(1/sinθ) حل کریں

$$\gamma = ( \frac { 1 } { \sin \theta } )$$

θ کے لئے حل کریں (complex solution)

$$\theta =2\pi n_{1}-i\ln(\frac{i\left(\sqrt{1-\gamma ^{2}}+1\right)}{\gamma })\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =2\pi n_{2}-i\ln(\frac{-i\sqrt{1-\gamma ^{2}}+i}{\gamma })\text{, }n_{2}\in \mathrm{Z}\text{, }\gamma \neq 0$$

γ کے لئے حل کریں

$$\gamma =\frac{1}{\sin(\theta )}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}$$

θ کے لئے حل کریں

$$\theta =arcSin(\gamma ^{-1})+2n_{10}\pi \text{, }n_{10}\in \mathrm{Z}$$

$$\theta =\pi +2n_{19}\pi +\left(-1\right)arcSin(\gamma ^{-1})\text{, }n_{19}\in \mathrm{Z}$$