4 cos² x + sin x = 1

sin(x)+2cos(2x)+2=1[latex] -sin^{2}[/latex](x)+sin(x)+2[latex]cos^{2} [/latex](x)+2=1[latex] frac{1}{2} [/latex][latex] ie^{-ix}- frac{1}{2}ie^{ix}+e^{-2ix}+e^{2ix}+2=1[/latex]x=2([latex] pi [/latex]n+[latex] tan^{-1}( frac{1}{3} (-4- sqrt{7}))), n∈Z[/latex]x=2([latex] pi n+ tan^{-1} ( frac{1}{3}( sqrt{7}-4))), n∈Z[/latex]x=[latex] frac{1}{2}(4 pi n+ pi ), n∈Z[/latex]