Solve alpha=a2ctan(-alpha3)

$$\alpha = a 2 c \tan ( - \alpha 3 )$$

Solve for a_2

$$\left\{\begin{matrix}a_{2}=-\frac{\alpha \cot(\alpha _{3})}{c}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(\alpha _{3}>\frac{\pi n_{2}}{2}\text{ and }\alpha _{3}<\frac{\pi n_{2}}{2}+\frac{\pi }{2}\right)\text{ and }c\neq 0\\a_{2}\in \mathrm{R}\text{, }&\left(c=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }\alpha _{3}=\pi n_{1}\right)\text{ and }\exists n_{3}\in \mathrm{Z}\text{ : }\left(\alpha _{3}>\pi n_{3}+\frac{\pi }{2}\text{ and }\alpha _{3}<\pi n_{3}+\frac{3\pi }{2}\right)\text{ and }\alpha =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$a_{2}c\tan(-\alpha _{3})=\alpha$$

The equation is in standard form.

$$c\tan(-\alpha _{3})a_{2}=\alpha$$

Divide both sides by c\tan(-\alpha _{3}).

$$\frac{c\tan(-\alpha _{3})a_{2}}{c\tan(-\alpha _{3})}=\frac{\alpha }{c\tan(-\alpha _{3})}$$

Dividing by c\tan(-\alpha _{3}) undoes the multiplication by c\tan(-\alpha _{3}).

$$a_{2}=\frac{\alpha }{c\tan(-\alpha _{3})}$$

Divide \alpha by c\tan(-\alpha _{3}).

$$a_{2}=-\frac{\alpha \cot(\alpha _{3})}{c}$$

Solve for c

$$\left\{\begin{matrix}c=-\frac{\alpha \cot(\alpha _{3})}{a_{2}}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(\alpha _{3}>\frac{\pi n_{2}}{2}\text{ and }\alpha _{3}<\frac{\pi n_{2}}{2}+\frac{\pi }{2}\right)\text{ and }a_{2}\neq 0\\c\in \mathrm{R}\text{, }&\left(a_{2}=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }\alpha _{3}=\pi n_{1}\right)\text{ and }\exists n_{3}\in \mathrm{Z}\text{ : }\left(\alpha _{3}>\pi n_{3}+\frac{\pi }{2}\text{ and }\alpha _{3}<\pi n_{3}+\frac{3\pi }{2}\right)\text{ and }\alpha =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$a_{2}c\tan(-\alpha _{3})=\alpha$$

The equation is in standard form.

$$a_{2}\tan(-\alpha _{3})c=\alpha$$

Divide both sides by a_{2}\tan(-\alpha _{3}).

$$\frac{a_{2}\tan(-\alpha _{3})c}{a_{2}\tan(-\alpha _{3})}=\frac{\alpha }{a_{2}\tan(-\alpha _{3})}$$

Dividing by a_{2}\tan(-\alpha _{3}) undoes the multiplication by a_{2}\tan(-\alpha _{3}).

$$c=\frac{\alpha }{a_{2}\tan(-\alpha _{3})}$$

Divide \alpha by a_{2}\tan(-\alpha _{3}).

$$c=-\frac{\alpha \cot(\alpha _{3})}{a_{2}}$$