3. Given $x \in[0,2 \pi]$, and $2 \cos x \leqslant|\sqrt{1+\sin 2 x}-\sqrt{1-\sin 2 x}| \leqslant \sqrt{2}, x$ the range of values for $x$ is $\qquad$
3. $\left[\frac{\pi}{4}, \frac{7 \pi}{4}\right]$.

Let $y=|\sqrt{1+\sin 2 x}-\sqrt{1-\sin 2 x}|=|| \sin x+\cos x|-| \sin x-\cos x||$, and discuss the following intervals: $\left[0, \frac{\pi}{4}\right],\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right],\left[\frac{3 \pi}{4}, \frac{5 \pi}{4}\right],\left[\frac{5 \pi}{4}, \frac{7 \pi}{4}\right],\left[\frac{7 \pi}{4}, 2 \pi\right]$. We can obtain that the range of $x$ is $\left[\frac{\pi}{4}, \frac{7 \pi}{4}\right]$.