Squared Trigonometric Functions

Algebra Level 2

θ \theta is an angle such that 180<θ<270180^\circ < \theta < 270^\circ, and sinθ=1213\sin \theta = \frac{-12}{13}. What is the value of

180(sin2θ2+cos2θ2+tan2θ2)?180 \left( \sin^2 \frac{\theta}{2} + \cos^2 \frac{\theta}{2} + \tan^2 \frac{\theta}{2} \right)?

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