In $\triangle A B C$, with the usual notations, if $\left(\tan \frac{A}{2}\right)\left(\tan \frac{B}{2}\right)=\frac{3}{4}$ then $a+b=\ldots \ldots$

In $\triangle A B C$, with the usual notations, if $\sin B \sin C=\frac{b c}{a^2}$, then the triangle is. ...........

If $R$ is the circum radius of $\triangle A B C$, then $A(\triangle A B C)=\ldots \ldots$

In $\triangle A B C$, if $\tan A+\tan B+\tan C=6$ and $\tan A \cdot \tan B=2$ then $\tan C=$ ...........