The number of solutions of the equation $2 \theta - \cos^{2} \theta + \sqrt{2} = 0$ is equal to

If the solutions for $\theta$ of $\cos p\theta + \cos q\theta = 0$ with $p > 0, q > 0$ are in an $A.P.$,then the numerically smallest common difference of the $A.P.$ is

The number of all values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ satisfying the equation $(1-\tan \theta)(1+\tan \theta) \sec ^2 \theta+2 \tan ^2 \theta=0$ is

The values of $\theta$ satisfying $\sin 7\theta = \sin 4\theta - \sin \theta$ and $0 < \theta < \frac{\pi}{2}$ are

If $\sqrt{2} \sec \theta + \tan \theta = 1,$ then the general value of $\theta$ is

The solution set of the trigonometric equation $\tan \theta + 5 \cot \theta = \sec \theta$ is