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 $\sin 2\theta = - 2$ (Not Possible) $\Rightarrow 2\theta = {\pi \over 2},{{5\pi } \over 2},{{9\pi } \over 2},{{13\pi } \over 2}$ $\Rightarrow \theta = {\pi \over 4},{{5\pi } \over 4},{{9\pi } \over 4},{{13\pi } \over 4}$ $\Rightarrow S = {\pi \over 4} + {{5\pi } \over 4} + {{9\pi } \over 4} + {{13\pi } \over 4} = 7\pi$ $\Rightarrow {{8S} \over \pi } = {{8 \times 7\pi } \over \pi } = 56.00$