The number of solutions of the equation $\sqrt[3]{\sin \theta - 1} + \sqrt[3]{\sin \theta} + \sqrt[3]{\sin \theta + 1} = 0$ in the interval $[0, 4\pi]$ is:

The general solution of $\sin x + \cos x = \min_{a \in \mathbb{R}} \{1, a^2 - 4a + 6\}$ is

The sum of solutions in $x \in (0, 2\pi)$ of the equation $4\cos(x)\cos\left(\frac{\pi}{3} - x\right)\cos\left(\frac{\pi}{3} + x\right) = 1$ is equal to: (in $\pi$)

The solution of the equation $4\cos^2 x + 6\sin^2 x = 5$ is:

If $\theta \in \left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]$,then the number of solutions of $\sqrt{3} \operatorname{cosec}^2 \theta - 2(\sqrt{3}-1) \operatorname{cosec} \theta - 4 = 0$ is equal to

The number of solutions of the trigonometric equation $1+\cos x \cdot \cos 5 x=\sin ^2 x$ in $[0, 2 \pi]$ is