8 sin 3x cos 3x больше = 2sqrt3

[latex]8\sin3x\cos3x\geq2\sqrt3;\\ 4\cdot2\sin3x\cos3x\geq2\sqrt3;\\ 4\cdot\sin6x\geq2\sqrt3;\\ \sin6x\geq\frac{2\sqrt3}{4};\\ \sin6x\geq\frac{\sqrt3}{2};\\ \frac{\pi}{3}+2\pi n\leq6x\leq\frac{2\pi}{3}+2\pi n,\ \ \ n\in Z;\\ \frac{\pi}{18}+\frac{\pi n}{3}\leq x\leq\frac{2\pi}{18}+\frac{\pi n}{3},\ \ \ n\in Z;\\\\ x\in\left[\frac{\pi}{18}+\frac{\pi n}{3};\frac{\pi}{9}+\frac{\pi n}{3}\right],\ \ \ n\in Z.[/latex]