Points of intersection with polar equations

[n00neimp0rtnt]

Homework Statement

I have to find all of the points of intersection of the curves...

r² = sin(2θ)
r² = cos(2θ)

The Attempt at a Solution

sin(2θ) = cos(2θ)
2sinθcosθ = cos²θ - sin²θ
2sinθcosθ - cos²θ = -sin²θ
cosθ(2sinθ - cosθ) = -sin²θ

This is where I'm having a problem, I'm not sure what to do from here.

 

[rock.freak667]

Why not just divide by cos2θ and solve tan2θ=1?

 

[n00neimp0rtnt]

Aww. Yep you're right, thanks. (Today is not a math day for me; I temporarily forgot how to factor earlier, haha)