[tex]\it x\in(0,\ \pi) \Rightarrow sinx\ne 0\ \ \ \ \ \ (*)\\ \\ \\ sin2x+2sin^2x=0 \Rightarrow 2sinxcosx+2sin^2x=0 \Rightarrow \\ \\ \Rightarrow 2sinx(cosx+sinx)=0\ \stackrel{(*)}{\Longrightarrow}\ cosx+sinx=0 \Rightarrow \\ \\ \Rightarrow cosx=-sinx\ \stackrel{(*)}{\Longrightarrow}\ x=\dfrac{3\pi}{4}[/tex]
