$x = \cos \theta - \cos 2\theta ,y = \sin \theta - \sin 2\theta$

Here, $x = \cos \theta - \cos 2\theta$ ..(i)
and $y = \sin \theta - \sin 2\theta$ …(ii)
Differentiating (i) \& (ii) w.r.t. $\theta$ , we get

$\cfrac{{dx}}{{d\theta }} = - \sin \theta - ( - \sin 2\theta ) \cdot 2$

$\cfrac{{dy}}{{d\theta }} = \cos \theta - \cos 2\theta \cdot 2 = \cos \theta - 2\cos 2\theta$

therefore, $\cfrac{{dy}}{{dx}} = \cfrac{{dy/d\theta }}{{dx/d\theta }} = \cfrac{{\cos \theta - 2\cos 2\theta }}{{2\sin 2\theta - \sin \theta }}$