In a triangle ABC with usual notations, if $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in arithmetic progression, then, $\tan \frac{\mathrm{A}}{2} \cdot \tan \frac{\mathrm{C}}{2}=$

If $\tan 3 \theta=\cot \theta$, then $\theta=$

The shaded region in the following figure represents a solution set of

With usual notations, in a triangle $A B C$, if $\theta$ is any real number, then $a \cos (B-\theta)+b \cos (A+\theta)$ is