If $(1-\cot A)(1-\cot B)=2$ then 

$\begin{array}{l}(1-\cot A)(1-\cot B)=2\\ \Rightarrow 1-\cot A-\cot B+\cot A\cot B=2\\ \Rightarrow \cot A\cot B-1=\cot A+\cot B\\ \Rightarrow \frac{\cot A\cot B-1}{\cot A+\cot B}=1\\ \Rightarrow \cot (A+B)=\cot 45°\\ \Rightarrow A+B=\frac{\pi }{4}\end{array}$