Sinefull trigonometry

Geometry Level 3

Let $$\theta_{1} =\dfrac{2\pi}{3}$$ , $$\theta_{2}=\dfrac{4\pi}{7}$$, $$\theta_{3}=\dfrac{7\pi}{12}$$. Then which of the following is true?

A. $$(\sin \theta_1)^{\sin \theta_1} < (\sin \theta_2)^{\sin \theta_2} < (\sin \theta_3)^{\sin \theta_3}$$

B. $$(\sin \theta_2)^{\sin \theta_2} < (\sin \theta_1)^{\sin \theta_1} < (\sin \theta_3)^{\sin \theta_3}$$

C. $$(\sin \theta_3)^{\sin \theta_3} < (\sin \theta_1)^{\sin \theta_1} < (\sin \theta_2)^{\sin \theta_2}$$

D. $$(\sin \theta_1)^{\sin \theta_1} < (\sin \theta_3)^{\sin \theta_3} < (\sin \theta_2)^{\sin \theta_2}$$

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