If $$\sin ^4 \theta \cos ^2 \theta=\sum_\limits{n=0}^{\infty} a_{2 n} \cos 2 n \theta$$, then the least $$n$$ for which $$a_{2 n}=0$$ is

If $$\sin \theta=-\frac{3}{4}$$, then $$\sin 2 \theta=$$

$$\begin{aligned} & \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\ldots +\frac{1}{\sin 89^{\circ}+\sin 90^{\circ}}= \end{aligned}$$

Which of the following trigonometric values are negative?

I. $$\sin \left(-292^{\circ}\right)$$

II. $$\tan \left(-190^{\circ}\right)$$

III. $$\cos \left(-207^{\circ}\right)$$

IV. $$\cot \left(-222^{\circ}\right)$$