G5.4 If $\cos ^{6} \theta+\sin ^{6} \theta=0.4$ and $d=2+5 \cos ^{2} \theta \sin ^{2} \theta$, find the value of $d$.
$\begin{array}{l}\left(\cos ^{2} \theta+\sin ^{2} \theta\right)\left(\cos ^{4} \theta-\sin ^{2} \theta \cos ^{2} \theta+\cos ^{4} \theta\right)=0.4 \\ \cos ^{4} \theta+2 \sin ^{2} \theta \cos ^{2} \theta+\cos ^{4} \theta-3 \sin ^{2} \theta \cos ^{2} \theta=0.4 \\ \left(\cos ^{2} \theta+\sin ^{2} \theta\right)^{2}-3 \sin ^{2} \theta \cos ^{2} \theta=0.4 \\ 1-0.4=3 \sin ^{2} \theta \cos ^{2} \theta \\ \sin ^{2} \theta \cos ^{2} \theta=0.2 \\ d=2+5 \cos ^{2} \theta \sin ^{2} \theta=2+5 \times 0.2=3\end{array}$