The value of the expression 2(sin6θ + cos6θ) - 3(sin4θ + cos4θ) + 1 is?

Answer: Option B

$$\text{ 2}\left({\sin }^6\theta +\text{co}{\text{s}}^6\theta \right)-\text{3}\left({\sin }^4\theta +\text{co}{\text{s}}^4\theta \right)\text{ + 1}$$
$$\Rightarrow \text{2}\left(1-3{\sin }^2\theta \text{co}{\text{s}}^2\theta \right)-$$     $$\text{3}\left(1-2{\sin }^2\theta c\text{o}{\text{s}}^2\theta \right)\text{ + }$$     $$\text{1}$$
$$\begin{array}{rl}& \Rightarrow \text{ 2}-6{\sin }^2\theta .\text{co}{\text{s}}^2\theta -3+6{\sin }^2\theta .\text{co}{\text{s}}^2\theta \text{ + 1}\\ & \Rightarrow 2-3+1\\ & \Rightarrow 0\end{array}$$