If $x=\alpha$ satisfies the equation $\frac{{\sin }^{-1}\left(x^{2022}\right)+2{\cos }^{-1}\left(x^{2021}\right)}{{\cos }^{-1}\left(x^{2022}\right)+2{\sin }^{-1}\left(x^{2021}\right)}=\frac{-5}{2}$  then the value of $\frac{{\sin }^{-1}\left(\sin \alpha \right)+{\tan }^{-1}\left(\tan \alpha \right)}{{\cos }^{-1}\left(\cos \alpha \right)+2\cos e{c}^{-1}\left(\cos ec\alpha \right)}$  is _______

Applying c and d
 $$\begin{gathered} \frac{\frac{\pi }{2}+2\times \frac{\pi }{2}}{{\sin }^{-1}{x}^{2022}-{\cos }^{-1}{x}^{2022}}+2\{{\cos }^{-1}{x}^{2021}-{\sin }^{-1}{x}^{2021}\}=\frac{-3}{-7} \\ \frac{\frac{3\pi }{2}}{4{\cos }^{-1}{x}^{2021}}-2{\cos }^{-1}{x}^{2022}-\frac{\pi }{2}=\frac{3}{7} \\ \Rightarrow \frac{7\pi }{2}=4{\cos }^{-1}{x}^{2021}-2{\cos }^{-1}{x}^{2022}-\frac{\pi }{2} \\ 2{\cos }^{-1}{x}^{2021}=2\pi +{\cos }^{-1}{x}^{2022} \\ x=1\&-1 \end{gathered}$$
$x=-1$  satisfies original equation 
So,  $\frac{{\sin }^{-1}\left(\sin \alpha \right)+{\tan }^{-1}\left(\tan \alpha \right)}{{\cos }^{-1}\left(\cos \alpha \right)+2\cos e{c}^{-1}\left(\cos ec\alpha \right)}=2$