Solve sina/1+cosalpha+1+cosa/sina=2csca

$$\frac { \sin a } { 1 + \cos \alpha } + \frac { 1 + \cos a } { \sin a } = 2 \csc a$$

Solve for a

$$a=2\pi n_{3}-\alpha \text{, }n_{3}\in \mathrm{Z}\text{, }\exists n_{4}\in \mathrm{Z}\text{ : }\left(\alpha >2\pi n_{3}-\pi n_{4}-\pi \text{ and }\alpha <2\pi n_{3}-\pi n_{4}\right)$$

$$a=2\pi n_{2}+\alpha \text{, }n_{2}\in \mathrm{Z}\text{, }\exists n_{4}\in \mathrm{Z}\text{ : }\left(\alpha >\pi n_{4}-2\pi n_{2}\text{ and }\alpha <\pi +\pi n_{4}-2\pi n_{2}\right)\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =2\pi n_{1}+\pi$$

Solve for α

$$\alpha =2\pi n_{2}+a\text{, }n_{2}\in \mathrm{Z}\text{, }\exists n_{1}\in \mathrm{Z}\text{ : }\left(a>2\pi n_{1}-2\pi n_{2}+\pi \text{ and }a<2\pi n_{1}-2\pi n_{2}+3\pi \right)$$

$$\alpha =2\pi n_{3}-a\text{, }n_{3}\in \mathrm{Z}\text{, }\exists n_{1}\in \mathrm{Z}\text{ : }\left(a>-2\pi n_{1}+2\pi n_{3}-3\pi \text{ and }a<-2\pi n_{1}+2\pi n_{3}-\pi \right)\text{, }\exists n_{4}\in \mathrm{Z}\text{ : }\left(a>\pi n_{4}\text{ and }a<\pi n_{4}+\pi \right)$$