Let S be the sum of all solutions (in radian) of the equation ${\sin }^4\mathrm{\theta }+{\cos }^4\mathrm{\theta }-\sin \mathrm{\theta }\cos \mathrm{\theta }=0\text{ in }[0,4\mathrm{\pi }]$Then $\frac{8\mathrm{S}}{\mathrm{\pi }}$is equal to _____.

Given equation 
$\begin{array}{l}{\sin }^4\mathrm{\theta }+{\cos }^4\mathrm{\theta }-\sin \mathrm{\theta cos}\mathrm{\theta }=0\\ \Rightarrow 1-{\sin }^2{\mathrm{\theta cos}}^2\mathrm{\theta }-\sin \mathrm{\theta cos}\mathrm{\theta }=0\\ \Rightarrow 2-(\sin 2\mathrm{\theta }{)}^2-\sin 2\mathrm{\theta }=0\\ \Rightarrow (\sin 2\mathrm{\theta }{)}^2+(\sin 2\mathrm{\theta })-2=0\\ \Rightarrow (\sin 2\mathrm{\theta }+2)(\sin 2\mathrm{\theta }-1)=0\\ \Rightarrow \sin 2\mathrm{\theta }=1\text{ or }\frac{\sin 2\mathrm{\theta }=-2}{\text{ (not possible) }}\\ \Rightarrow 2\mathrm{\theta }=\frac{\mathrm{\pi }}{2},\frac{5\mathrm{\pi }}{2},\frac{9\mathrm{\pi }}{2},\frac{13\mathrm{\pi }}{2}\\ \Rightarrow \mathrm{\theta }=\frac{\mathrm{\pi }}{4},\frac{5\mathrm{\pi }}{4},\frac{9\mathrm{\pi }}{4},\frac{13\mathrm{\pi }}{4}\\ \Rightarrow \mathrm{S}=\frac{\mathrm{\pi }}{4}+\frac{5\mathrm{\pi }}{4}+\frac{9\mathrm{\pi }}{4}+\frac{13\mathrm{\pi }}{4}=7\mathrm{\pi }\\ \Rightarrow \frac{8\mathrm{S}}{\mathrm{\pi }}=\frac{8\times 7\mathrm{\pi }}{\mathrm{\pi }}=56.00\end{array}$