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]