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Let
\[
\begin{aligned}
\Delta(x)= & \left|\begin{array}{lll}
\cos 2 x & \sin ^{2} x & \cos 4 x \\
\sin ^{2} x & \cos 2 x & \cos ^{2} x \\
\cos 4 x & \cos ^{2} x & \cos 2 x
\end{array}\right| \\
& =a_{0}+a_{1} \sin x+a_{2} \sin ^{2} x+\ldots
\end{aligned}
\]
then
(a) \( a_{0}=-1 \)
(b) \( a_{1}=0 \)
(c) \( a_{2}=12 \)
(d) \( a_{1}=5 \)
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