Let S be the sum of all solutions

Given equation

$\sin ^{4} \theta+\cos ^{4} \theta-\sin \theta \cos \theta=0$

$\Rightarrow 1-\sin ^{2} \theta \cos ^{2} \theta-\sin \theta \cos \theta=0$

$\Rightarrow 2-(\sin 2 \theta)^{2}-\sin 2 \theta=0$

$\Rightarrow(\sin 2 \theta)^{2}+(\sin 2 \theta)-2=0$

$\Rightarrow(\sin 2 \theta+2)(\sin 2 \theta-1)=0$

$\Rightarrow \sin 2 \theta=1$ or $\frac{\sin 2 \theta=-2}{\text { (not posible) }}$

$\Rightarrow 2 \theta=\frac{\pi}{2}, \frac{5 \pi}{2}, \frac{9 \pi}{2}, \frac{13 \pi}{2}$

$\Rightarrow \theta=\frac{\pi}{4}, \frac{5 \pi}{4}, \frac{9 \pi}{4}, \frac{13 \pi}{4}$

$\Rightarrow S=\frac{\pi}{4}+\frac{5 \pi}{4}+\frac{9 \pi}{4}+\frac{13 \pi}{4}=7 \pi$

$\Rightarrow \frac{8 S}{\pi}=\frac{8 \times 7 \pi}{\pi}=56.00$