Need help solving this equation −sin (2θ) − cos (4θ) = 0

Can someone help explain to me how to use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). I have tried for some time and have been having quite of bit of difficulty on figuring out how to proceed. Any input will be sincerely appreciated.

Re: Need help solving this equation −sin (2θ) − cos (4θ) = 0

To make things simpler perhaps, I would suggest letting where and so the equation becomes:

I would suggest using the double-angle identity for cosine this was you will obtain a quadratic in which factors nicely.

Can you proceed?