Решить неравенство: sin2x*sin(x/2) - cos2x*cos(x/2) > 1/2

\frac{1}2" alt="sin2x*sin\frac{x}{2} - cos2x*cos\frac{x}{2}>\frac{1}2" align="absmiddle" class="latex-formula">

$cos2x*cos\frac{x}{2}-sin2x*sin\frac{x}{2}<-\frac{1}2$

$cos(2x+\frac{x}{2})<-\frac{1}{2}$

$cos(\frac{4x}2+\frac{x}{2})<-\frac{1}2$

$cos(\frac{5x}2)<-\frac{1}2$

$\frac{2\pi}3+2*\pi*n<\frac{5x}2<\frac{4\pi}3+2*\pi*n; neZ$

$\frac{4\pi}3+4*\pi*n<5x<\frac{8\pi}3+4*\pi*n; neZ$

$\frac{4\pi}{15}+\frac{4}5*\pi*n<x<\frac{8\pi}{15}+\frac{4}5*\pi*n; neZ$