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The smallest value of $5 \cos \theta + 12$ is

If in a $\Delta ABC$,$\sin^3 A + \sin^3 B + \sin^3 C = 3 \sin A \cdot \sin B \cdot \sin C$,then:

If $\sin \theta_1 + \sin \theta_2 + \sin \theta_3 = 3$,then $\cos \theta_1 + \cos \theta_2 + \cos \theta_3 =$

If $A+B+C=180^{\circ}$,then the value of $\tan \left(\frac{A}{2}\right) \tan \left(\frac{B}{2}\right)+\tan \left(\frac{B}{2}\right) \tan \left(\frac{C}{2}\right)+\tan \left(\frac{C}{2}\right) \tan \left(\frac{A}{2}\right)$ is

The minimum value of $2 \sin^2 \theta + 8 \csc^2 \theta$ is (where $\theta \in R$):-

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