If $A + C = B$,then $\tan A \tan B \tan C = $

If $\sin \alpha = 1/\sqrt{5}$ and $\sin \beta = 3/5$,then $\beta - \alpha$ lies in the interval

If $\cos \alpha + \cos \beta = \frac{1}{3}$ and $\sin \alpha + \sin \beta = \frac{1}{4}$,then $\cos (\alpha + \beta) = $

If $\cot \alpha = 1$ and $\sec \beta = -\frac{5}{3}$,where $\pi < \alpha < \frac{3\pi}{2}$ and $\frac{\pi}{2} < \beta < \pi$,then the value of $\tan(\alpha + \beta)$ and the quadrant in which $\alpha + \beta$ lies,respectively,are

If $(1+\tan \alpha)(1+\tan 4 \alpha)=2$ and $\alpha \in \left(0, \frac{\pi}{16}\right)$,then $\alpha$ is equal to

For $\theta \in \left(0, \frac{\pi}{2}\right)$,if $\tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1$,then $\theta =$