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$\frac{1+\cos \theta-\sin \theta}{1+\cos \theta+\sin \theta}+\frac{1+\cos \theta+\sin \theta}{1+\cos \theta-\sin \theta}=$

Let $A, B, C$ be three angles such that $\sin A + \sin B + \sin C = 0$. Then,the value of $\frac{\sin A \sin B \sin C}{\sin 3A + \sin 3B + \sin 3C}$ (wherever defined) is:

If $(\sin \theta - \operatorname{cosec} \theta)^2 + (\cos \theta + \sec \theta)^2 = 5$ and $\theta$ lies in the third quadrant,then $(\sin \theta + \cos \theta)^3 = $

If $\alpha = 22^\circ 30'$,then $(1 + \cos \alpha )(1 + \cos 3\alpha )(1 + \cos 5\alpha )(1 + \cos 7\alpha )$ equals

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