7. (2005 National High School Mathematics League Sichuan Preliminary Contest Question) Let $0 \leqslant x \leqslant 2 \pi$, then the range of $x$ that satisfies the inequality $\sin \left(x-\frac{\pi}{6}\right)>\cos x$ is $\qquad$ .
7. Solution: From $\sin \left(x-\frac{\pi}{6}\right)>\cos x$, we get $\sin \left(x-\frac{\pi}{3}\right)>0$, solving this yields $\frac{\pi}{3}<x<\frac{4 \pi}{3}$.