If $\sin \theta ,\cos \theta ,\tan \theta$ are in G.P., then the value of ${\cot }^6\theta -{\cot }^2\theta$ is

$$\begin{gathered} {\cos }^2\theta =\sin \theta \tan \theta (\because \sin \theta ,\cos \theta ,\tan \theta areinG.P) \\ Co{s}^2\theta =\frac{{\sin }^2\theta }{\cos \theta }\Rightarrow {\cot }^2\theta =\sec \theta , \\ Co{t}^4\theta ={\sec }^2\theta \\ \Rightarrow {\cot }^4\theta =1+{\tan }^2\theta \\ \Rightarrow {\cot }^4\theta =1+\frac{1}{{\cot }^2\theta }={\cot }^6\theta -{\cot }^2\theta =1 \end{gathered}$$