What is the number of roots of the quadratic equation $8\sec^2\theta - 6\sec\theta + 1 = 0$?

If the sum of all the solutions of the equation $8 \cos x \cdot \left( \cos \left( \frac{\pi}{6} + x \right) \cdot \cos \left( \frac{\pi}{6} - x \right) - \frac{1}{2} \right) = 1$ in the interval $[0, \pi]$ is $k\pi$,then $k$ is equal to:

The number of solutions of the equation $\sin^{65}x - \cos^{65}x = -1$ for $x \in (-\pi, \pi)$ is:

The number of solutions of the equation $\cos 2 \theta \cos \frac{\theta}{2} + \cos \frac{5 \theta}{2} = 2 \cos^3 \frac{5 \theta}{2}$ in the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is:

If $x \neq (2n+1) \frac{\pi}{4}$,then the general solution of $\cos x + \cos 3x = \sin x + \sin 3x$ is

The number of solutions of the trigonometric equation $2 \tan 2 \theta - \cot 2 \theta + 1 = 0$ lying in the interval $[0, \pi]$ is