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

Given equation <br><br>${\sin ^4}\theta + {\cos ^4}\theta - \sin \theta \cos \theta = 0$<br><br>$\Rightarrow 1 - {\sin ^2}\theta {\cos ^2}\theta - \sin \theta \cos \theta = 0$<br><br>$\Rightarrow 2 - {(\sin 2\theta )^2} - \sin 2\theta = 0$<br><br>$\Rightarrow {(\sin 2\theta )^2} + (\sin 2\theta ) - 2 = 0$<br><br>$\Rightarrow (\sin 2\theta + 2)(\sin 2\theta - 1) = 0$<br><br>$\Rightarrow \sin 2\theta = 1$ or $\sin 2\theta = - 2$ (Not Possible)<br><br>$$ \Rightarrow 2\theta = {\pi \over 2},{{5\pi } \over 2},{{9\pi } \over 2},{{13\pi } \over 2}$$<br><br>$$ \Rightarrow \theta = {\pi \over 4},{{5\pi } \over 4},{{9\pi } \over 4},{{13\pi } \over 4}$$<br><br>$$ \Rightarrow S = {\pi \over 4} + {{5\pi } \over 4} + {{9\pi } \over 4} + {{13\pi } \over 4} = 7\pi $$<br><br>$\Rightarrow {{8S} \over \pi } = {{8 \times 7\pi } \over \pi } = 56.00$