Solve the equation :$\tan 2x=-\cot (x+\large\frac{\pi}{6})$

Question

$\begin{array}{1 1}(A)\;n\pi+ \large\frac{2\pi}{3}&(B)\;n\pi\pm \large\frac{\pi}{6}\\(C)\;n\pi\pm \large\frac{\pi}{8}&(D)\;2n\pi\pm \large\frac{3\pi}{4}\end{array} $