Explanation

(c)
$6(\sin^{6}{\theta + \cos^{6}{\theta) - 9\ (\sin^{4}{\theta + \cos^{4}{\theta) + 4}}}}$
$= 6\left\lbrack \left( \sin^{2}{\theta + \cos^{2}\theta} \right)^{3} - 3\sin^{2}{\theta\cos^{2}{\theta\ (\sin^{2}{\theta + \cos^{2}{\theta)}}}} \right\rbrack - 9\left\lbrack {{(sin}^{2}{\theta + \cos^{2}{\theta)}}}^{2} - 2\sin^{2}{\theta\cos^{2}\theta} \right\rbrack + 4$
$= - 6\left\lbrack 1 - 3\ \sin^{2}{\theta\cos^{2}\theta} \right\rbrack - 9\left( 1 - 2\ \sin^{2}{\theta\cos^{2}\theta} \right) + 4$
$= 6 - 9 + 4 = 1$