How do I find $\displaystyle r$ and $\displaystyle \theta$ for $\displaystyle \bar{z} = z^2$?

If I convert to polar form, I get

$\displaystyle r(cos\theta - isin\theta) = r^2(cos\theta + isin\theta)^2$

$\displaystyle \equiv cos\theta - isin\theta = r(cos(2\theta)+isin(2\theta))$

Am I trying to equate the real and imaginary parts of the two sides of the equation? If so, how does the r on the RHS affect this? or can I assume it is 1 and say

$\displaystyle cos\theta = cos(2\theta)$ and $\displaystyle -sin\theta = sin(2\theta) $?

How do I proceed?