How Do You Solve cosθ = sin2θ/2 Using Trigonometric Identities?

[theintarnets]

Homework Statement

cosθ = sin²θ/2

Homework Equations

None.

The Attempt at a Solution

I really don't know what to do. I tried using the half and double angle identities and this is what I got:
cosθ = (1-cos2θ)/2
2cosθ = 1-cos2θ
2cosθ + cos2θ = 1
2cosθ + 2cos²θ -1 = 1
2(cosθ + cos²θ) = 2
cosθ + cos²θ = 1
cos²θ + cosθ - 1 = 0

I'm not sure if that can be factored, so I tried using the quadratic formula. I got (-1 ± √5)/2
What am I supposed to do now? I don't even know if I did this right. Someone pleeeaase help mee ):

 

[scurty]

Your very first step is wrong: $sin^2(\theta) \neq 1-cos(2\theta)$

I would suggest writing $sin^2(\theta)$ in terms of $cos^2(\theta)$ right from the start! You'll end up with a quadratic equation, similar in form as your last equation you gave (which is wrong!). When you solve this quadratic equation, what exactly is set equal to the answer?