Помогите решить уравнение 3sin^2x+sin2x+cos^2x=1

[latex]3sin^{2} x+sin2x+cos^{2} x=1 \\ 3sin^{2} x+2sinxcosx+cos^{2} x-1=0 \\ 3sin^{2} x+2sinxcosx+cos^{2} x-sin^{2} x-cos^{2} x=0 \\ 3sin^{2} x+2sinxcosx-sin^{2} x=0 \\ 2sin^{2} x+2sinxcosx=0 \\ 2(sin^{2} x+sinxcosx)=0/:2 \\ sin^{2} x+sinxcosx=0 \\ sinx(sinx+cosx)=0 \\ sinx=0 \\ x= \pi n \\ [/latex] [latex]sinx+cosx=0/:cosx \\ cosx \neq 0 \\ x \neq \frac{ \pi }{2}+ \pi a \\ tgx+1=0 \\ tgx=-1 \\ x=- \frac{ \pi }{4} + \pi m \\ [/latex] n ∈  Z m ∈  Z a   ∈ Z