13. (2004 National College Entrance Examination - Chongqing Paper) Find the smallest positive period and the minimum value of the function $y=\sin ^{4} x+2 \sqrt{3} \sin x \cos x-\cos ^{4} x$, and write down the intervals where the function is monotonically increasing on $[0, \pi]$.
Prove that connecting $A F$, let $\angle B A F=\alpha, \angle D A F=\beta, \angle B F A=\varphi, \angle D F A=\theta$.
13. $y=2 \sin \left(2 x-\frac{\pi}{6}\right)$. The smallest positive period is $\pi$, the minimum value is -2, the intervals of monotonic increase are $\left[0, \frac{\pi}{3}\right],\left[\frac{5}{6} \pi, \pi\right]$