inverse function

[man111]

find sum of values of $x$ which satisfy

$\cot^{-1}(x-2)+\cot^{-1}(3-x) = \cot^{-1}(x-12)$

where $\cot^{-1}(x) = arc \cot (x)$

[Praded]

$\ctg(\alpha+\beta)=\dfrac{\ctg\alpha\cdot\ctg\beta-1}{\ctg\alpha+\ctg\beta}$

[Dave]

$x_1=-1, x_2=5$. The sum is $4$.