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