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$\theta$ is an angle such that $180^\circ < \theta < 270^\circ$, and $\sin \theta = \frac{-12}{13}$. What is the value of

$180 \left( \sin^2 \frac{\theta}{2} + \cos^2 \frac{\theta}{2} + \tan^2 \frac{\theta}{2} \right)?$

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