If $\sin \theta + \cos \theta = 1$,then $\sin \theta \cos \theta = $

If $A, B, C, D$ are the angles of a cyclic quadrilateral,then $\cos A + \cos B + \cos C + \cos D = $

If $\tan \theta + \sin \theta = m$ and $\tan \theta - \sin \theta = n,$ then

If $\frac{1}{6} \sin \theta, \cos \theta, \tan \theta$ are in $G.P.$,then the general solution of $\theta$ is

Let $|\cos \theta \cos (60^{\circ}-\theta) \cos (60^{\circ}+\theta)| \leq \frac{1}{8}$, where $\theta \in [0, 2\pi]$. Then, the sum of all $\theta \in [0, 2\pi]$ where $\cos 3\theta$ attains its maximum value is: (in $\pi$)

If $2 \sec 2\alpha = \tan \beta + \cot \beta$,then one of the values of $\alpha + \beta$ is