If $\tan^{-1} \frac{\large x-1}{\large x-2} + \tan^{-1} \frac{\large x+1}{\large x+2} = \frac{\large \pi}{\large 4}$ then find the value of $x$

Question

$\begin{array}{1 1} \pm \frac{1}{\sqrt 2} \\ \frac{1}{\sqrt 2} \\ - \frac{1}{\sqrt 2} \\ \pm \sqrt 2 \end{array}$