tan^2x=sin2x, 0<=x<2pi

cosx cannot = 0 ; x cannot = pi/2 or 3pi/2

sin^2x/cos^2x=2sinxcosx

sin^2x=2sinxcos^3x

sin^2x-2sinxcos^3x=0

sinx(sinx-2cos^3x)=0

sinx=0 or sinx-2cos^3x=0

+-sqrt(1-cos^2x) - 2cos^3x=0

+-sqrt(1-cos^2x) = 2cos^3x

*square both sides to remove radical

1-cos^2x = 4cos^6x

4cos^6x-cos^2x-1=0

I don't know how to solve this equation, can someone please provide me with a link to read how to solve this equiation?