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If $A = \begin{bmatrix} 0 & -\tan\left(\dfrac{\theta}{2}\right) \ \tan\left(\dfrac{\theta}{2}\right) & 0 \end{bmatrix}$ and $(I_2 + A)(I_2 - A)^{-1} = \begin{bmatrix} a & -b \ b & a \end{bmatrix}$, then $13(a^2 + b^2)$ is equal to ______.
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