The value of the expression (cos6θ + sin6θ - 1)(tan2θ + cot2θ + 2) is:

Answer: Option A

$$\begin{array}{rl}& \left({\cos }^6\theta +{\sin }^6\theta -1\right)\left({\tan }^2\theta +{\cot }^2\theta +2\right)\\ & \text{Put }\theta =45^{\circ }\\ & =\left({\cos }^6{45}^{\circ }+{\sin }^6{45}^{\circ }-1\right)\left({\tan }^2{45}^{\circ }+{\cot }^2{45}^{\circ }+2\right)\\ & =\left(\frac{1}{8}+\frac{1}{8}-1\right)\left(1+1+2\right)\\ & =\frac{-3}{4}\times 4\\ & =-3\end{array}$$