The expression (cos6θ + sin6θ - 1)(tan2θ + cot2θ + 2) + 3 is equal to:

Answer: Option A

(cos⁶θ + sin⁶θ - 1)(tan²θ + cot²θ + 2) + 3
Put θ = 45°
= (cos⁶45° + sin⁶45° - 1)(tan²45° + cot²45° + 2) + 3
$$\begin{array}{rl}& =\left(\frac{1}{8}+\frac{1}{8}-1\right)\left(1+1+2\right)+3\\ & =-\frac{3}{4}\times 4+3\\ & =0\end{array}$$