find angle A

In any triangle $\triangle {ABC},\angle A+\angle B+\angle C=π$ , and so $\cot A\cot B+\cot B\cot C+\cot C\cot A=1$

From the given information, $\cot A+\cot B+\cot C=\sqrt 3\implies \cot^2 A+\cot^2 B+\cot^2 C+2(\cot A\cot B+\cot B\cot C+\cot C\cot A) =3$

$\implies \cot^2 A+\cot^2 B+\cot^2 C=3-2=1$

$\implies \cot^2 A+\cot^2 B+\cot^2 C-1=0$

$\implies \cot^2 A+\cot^2 B+\cot^2 C-\cot A\cot B-\cot B\cot C-\cot C\cot A=0$

$\implies \cot A=\cot B=\cot C\implies A=B=C=\dfrac {180\degree}{3}=\boxed {60\degree}$ .