Answer
$$W=-8 \cos ^{2}(2 x)-8 \sin^{2} (2 x).$$
Work Step by Step
$$W=\left| \begin {array}{ccc} 1&\sin \left( 2\,x \right) &\cos \left( 2
\,x \right) \\ 0&2\,\cos \left( 2\,x \right) &-2\,
\sin \left( 2\,x \right) \\ 0&-4\,\sin \left( 2\,x
\right) &-4\,\cos \left( 2\,x \right) \end {array} \right|=-8 \cos ^{2}(2 x)-8 \sin^{2} (2 x).
$$
