If $A=\left[\begin{array}{cc}0 & -\tan \left(\frac{\theta}{2}\right) \\ \tan \left(\frac{\theta}{2}\right) & 0\end{array}\right]$ and $\left(I_2+A\right)\left(I_2-A\right)^{-1}= \left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]$, then $13\left(a^2+b^2\right)$ is equal to $\_\_\_\_$ .
