If $\sin \left(x+\frac{\pi}{3}\right)+\sin \left(x-\frac{\pi}{3}\right)=1$,then find the value of $x$ in the interval $[0, \pi]$.

The general solution of $\sin x + \cos x = 1$ is

If $\alpha, \beta, \gamma$ and $\delta$ are the solutions of the equation $\tan \left( \theta + \frac{\pi}{4} \right) = 3 \tan 3\theta$,no two of which have equal tangents,then the value of $\tan \alpha + \tan \beta + \tan \gamma + \tan \delta$ is

The number of solutions of the equation $\cos 6x + \cos 4x + \cos 2x = -1$ in the interval $[0, \pi]$ is:

If $\alpha$,$-\frac{\pi}{2} < \alpha < \frac{\pi}{2}$ is the solution of $4 \cos \theta + 5 \sin \theta = 1$,then the value of $\tan \alpha$ is

The general solution of $\sin^{2} x \cdot \sec x = \tan x - \sin x + 1$ is