The value of 2 ( ^6 + ^6 ) - 3 ( ^4 + ^4 ) ^4 - ^4 - 2 ^2 is:

Answer: Option A

$$\begin{array}{rl}& \frac{2\left({\sin }^6\theta +{\cos }^6\theta \right)-3\left({\sin }^4\theta +{\cos }^4\theta \right)}{{\cos }^4\theta -{\sin }^4\theta -2{\cos }^2\theta }\\ & =\frac{2\left(1-3{\sin }^2\theta .{\cos }^2\theta \right)-3\left(1-2{\sin }^2\theta .{\cos }^2\theta \right)}{\left({\cos }^2\theta +{\sin }^2\theta \right)\left({\cos }^2\theta -{\sin }^2\theta \right)-2{\cos }^2\theta }\\ & =\frac{2-6{\sin }^2\theta .{\cos }^2\theta -3+6{\sin }^2\theta .{\cos }^2\theta }{-\left({\cos }^2\theta +{\sin }^2\theta \right)}\\ & =\frac{-1}{-1}\\ & =1\end{array}$$