The equation $\sin x\cos x = 2$ has

If $\frac{{\tan 3\theta - 1}}{{\tan 3\theta + 1}} = \sqrt 3 $, then the general value of $\theta $ is

Let $\theta \in [0, 4\pi ]$ satisfy the equation $(sin\, \theta + 2) (sin\, \theta + 3) (sin\, \theta + 4) = 6$ . If the sum of all the values of $\theta $ is of the form $k\pi $, then the value of $k$ is

Solve $\tan 2 x=-\cot \left(x+\frac{\pi}{3}\right)$

Let $S={\theta \in\left(0, \frac{\pi}{2}\right): \sum_{m=1}^{9}}$

$\sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}$ Then.

The number of real numbers $\lambda$ for which the equality $\frac{\sin (\lambda \alpha) \quad \cos (\lambda \alpha)}{\sin \alpha}=\lambda-1$,holds for all real $\alpha$ which are not integral multiples of $\pi / 2$ is