If $\cos (\alpha -\beta )+\cos (\beta -\gamma )+\cos (\gamma -\alpha )=3$, then the value of $\cot \alpha +\cot \beta +\cot \gamma$ is [where $\alpha ,\beta ,\gamma$ are the angles of a ${\Delta }^{le}$

$\begin{array}{l}\cos (\alpha -\beta )+\cos (\beta -\gamma )+\cos (\gamma -\alpha )=3\\ \text{Maximum value of} \cos \theta \text{\hspace{0.17em}is\hspace{0.17em}}1\\ \cos (\alpha -\beta )=1\\ \alpha -\beta =0\Rightarrow \alpha =\beta \\ \text{Similarly\hspace{0.17em}}\beta -\gamma =0\Rightarrow \beta =\gamma \\ \therefore \text{\hspace{0.17em}clearly a} {\Delta }^{le}\text{\hspace{0.17em}is equilateral\hspace{0.17em}}{\Delta }^{le}\\ \alpha =60°,\beta =60°,\gamma =60°\\ \cot \alpha +\cot \beta +\cot \gamma =\cot 60°+\cot 60°+\cot 60°\\ =3(\cot 60°)\\ =3\left(\frac{1}{\sqrt{3}}\right)\\ =\frac{3}{\sqrt{3}}=\sqrt{3}\end{array}$