Найдите число а ∈(π/2,π), если известно что tg2a= -12/5

[latex]tg(2a)=- \frac{12}{5} [/latex] [latex]2a=arctg(- \frac{12}{5})+ \pi k[/latex] [latex]a=- \frac{arctg(\frac{12}{5})}{2}+\frac{ \pi k}{2}[/latex] [latex]\frac{ \pi}{2}\ \textless \ - \frac{arctg(\frac{12}{5})}{2}+\frac{ \pi k}{2}\ \textless \ \pi [/latex] [latex]\frac{ \pi}{2}+\frac{arctg(\frac{12}{5})}{2}\ \textless \ \frac{ \pi k}{2}\ \textless \ \pi+\frac{arctg(\frac{12}{5})}{2}[/latex] [latex]1+\frac{arctg(\frac{12}{5})}{ \pi }\ \textless \ k\ \textless \ 2+\frac{arctg(\frac{12}{5})}{ \pi }[/latex] [latex]k=2[/latex] - целое число [latex]a=- \frac{arctg(\frac{12}{5})}{2}+ \pi[/latex]