pt$\Leftrightarrow (cosx+1)(cos2x-mcosx)-m(1-cos^2x)=0$$\Leftrightarrow (cosx+1)(cos2x-mcosx-m(1-cosx))=0$
$\Leftrightarrow (cosx+1)(cos2x-m)=0$
pt da cho co nghiem $x\in[0;\frac{2\pi}{3}]$ khi $cos2x=m $ co nghiem $x\in [0;2\pi/3]$
Ta co:$0\leq x\leq 2\pi/3\Leftrightarrow 0\leq 2x\leq 4\pi/3$
khi do $-1\leq cos2x\leq 1$hay $-1\leq m\leq 1$
Vay $m\in[-1;1]$