If in a triangle $A B C$, with usual notations, the angles are in A.P. and $b: c=\sqrt{3}: \sqrt{2}$, then angle $\mathrm{A}=$

The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm , is

If angle $\theta$ in $[0,2 \pi]$ satisfies both the equations $\cot \theta=\sqrt{3}$ and $\sqrt{3} \sec \theta+2=0$, then $\theta$ is equal to

The area of the triangle with vertices $(1,2,0)$, $(1,0,2)$ and $(0,3,1)$ is