The numbers $\frac{\sin x}{6},\cos xand\tan x$ will be in G.P if……………

${\cos }^{2}x=\frac{\sin x\tan x}{6}\Rightarrow 6{\cos }^{3}x+{\cos }^{2}x-1=0$

Put  $\cos x=t\Rightarrow 6t^3+t^2-1=0\Rightarrow (2t-1)(3t\text{'}+2t+1)=0$
As quadratic factor has imaginary root  $t=\frac{1}{2}is\cos x=\frac{1}{2}$
  $\Rightarrow x=\pm \frac{5}{3}+2k\pi ,k\in Z$