I can't figure how to convert this polar equation to a cartesian equation.
$\displaystyle r = 2 - \sin2\theta $
$\displaystyle r = 2 - \sin 2 \theta$ .............................simplify the double angle sine
$\displaystyle \Rightarrow r = 2 - 2 \sin \theta \cos \theta$ .................multiply through by $\displaystyle r^2$
$\displaystyle \Rightarrow r^3 = 2r^2 - 2r \sin \theta \cdot r \cos \theta$ ........now convert
$\displaystyle \Rightarrow \left( x^2 + y^2 \right)^{3/2} = 2x^2 + 2y^2 - 2xy$
and you can attempt to simplify that monstrosity if you so desire, i would leave it like that though