If $sin^2 θ = cos^3 θ$, then the value of $(cot^2 θ − cot^6 θ)$ is:

-1 0 2 1

-1

We are given that :- sin²θ = cos³θ   ----(1) Now, cot²θ - cot6 θ = cot²θ - \(\frac{cos6  θ}{sin6 θ}\) { on squaring equation 1 , sin4 θ = cos6 θ } = cot²θ - \(\frac{sin4 θ}{sin6 θ}\) = cot²θ - \(\frac{1}{sin² θ}\) = cot²θ - cosec²θ { using , cosec²θ - cot²θ = 1 } = - 1