$$ \begin{aligned} &\text { The value of }\\ &\begin{aligned} \sin ^{-1}\left(-\frac{1}{\sqrt{2}}\right)+\cos ^{-1} & \left(-\frac{1}{2}\right) -\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\tan ^{-1}(-\sqrt{3}) \text { is } \end{aligned} \end{aligned} $$

If triangle ABC is a right angled at A and $\tan \frac{\mathrm{B}}{2}$, $\tan \frac{\mathrm{C}}{2}$ are roots of the equation $a x^2+b x+c=0$, $\mathrm{a} \neq 0$, then

If $a^2+b^2+c^2=r^2$, then the value of $\tan ^{-1}\left(\frac{\mathrm{ab}}{\mathrm{cr}}\right)+\tan ^{-1}\left(\frac{\mathrm{bc}}{\mathrm{ar}}\right)+\tan ^{-1}\left(\frac{\mathrm{ca}}{\mathrm{br}}\right)=$