Solve sin^2alpha-sin^2beta=cos^2alpha-cos^2beta

$$\sin ^ { 2 } \alpha - \sin ^ { 2 } \beta = \cos ^ { 2 } \alpha - \cos ^ { 2 } \beta$$

Solve for α

$$\left\{\begin{matrix}\alpha =\pi n_{6}+\beta \text{, }n_{6}\in \mathrm{Z}\text{; }\alpha =\pi n_{7}-\beta \text{, }n_{7}\in \mathrm{Z}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\left(\beta \geq 2\pi n_{1}\text{ and }\beta \leq 2\pi n_{1}+\pi \right)\\\alpha =\pi n_{4}-\beta \text{, }n_{4}\in \mathrm{Z}\text{; }\alpha =\pi n_{5}+\beta \text{, }n_{5}\in \mathrm{Z}\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\beta =\pi n_{3}+\frac{\pi }{2}\\\alpha =\pi n_{4}-\beta \text{, }n_{4}\in \mathrm{Z}\text{; }\alpha =\pi n_{5}+\beta \text{, }n_{5}\in \mathrm{Z}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(\beta \geq 2\pi n_{2}+\pi \text{ and }\beta \leq 2\pi n_{2}+2\pi \right)\end{matrix}\right.$$

Solve for β

$$\left\{\begin{matrix}\beta =\pi n_{6}+\alpha \text{, }n_{6}\in \mathrm{Z}\text{; }\beta =\pi n_{7}-\alpha \text{, }n_{7}\in \mathrm{Z}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\left(\alpha \geq 2\pi n_{1}\text{ and }\alpha \leq 2\pi n_{1}+\pi \right)\\\beta =\pi n_{4}-\alpha \text{, }n_{4}\in \mathrm{Z}\text{; }\beta =\pi n_{5}+\alpha \text{, }n_{5}\in \mathrm{Z}\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\alpha =\pi n_{3}+\frac{\pi }{2}\\\beta =\pi n_{4}-\alpha \text{, }n_{4}\in \mathrm{Z}\text{; }\beta =\pi n_{5}+\alpha \text{, }n_{5}\in \mathrm{Z}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(\alpha \geq 2\pi n_{2}+\pi \text{ and }\alpha \leq 2\pi n_{2}+2\pi \right)\end{matrix}\right.$$