If the function f defined on $\left(\frac{\pi }{6},\frac{\pi }{3}\right)$by f\left( x \right) = \,\left\{ {\begin{array}{*{20}{c}}{\dfrac{{\sqrt 2 \cos x - 1}}{{\cot x - 1}},}{x \ne \dfrac{\pi}{4}} \\ {k,}{x = \dfrac{\pi }{4}} \end{array}} \right. is continuous, then k is equal to :