Squared Trigonometric Functions

Algebra Level 2

\( \theta\) 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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