First, find \(\frac{dx}{d\theta}\) and \(\frac{dy}{d\theta}\):

\(\frac{dx}{d\theta} = a(2 - 2\cos 2\theta) = 2a(1 - \cos 2\theta)\)

\(\frac{dy}{d\theta} = a(2\sin 2\theta)\)

Now, use the chain rule to find \(\frac{dy}{dx}\):

\(\frac{dy}{dx} = \frac{dy/d\theta}{dx/d\theta} = \frac{2a\sin 2\theta}{2a(1 - \cos 2\theta)}\)

Simplify the expression:

\(\frac{dy}{dx} = \frac{\sin 2\theta}{1 - \cos 2\theta}\)

Using the identity \(\sin 2\theta = 2\sin \theta \cos \theta\) and \(1 - \cos 2\theta = 2\sin^2 \theta\), we have:

\(\frac{dy}{dx} = \frac{2\sin \theta \cos \theta}{2\sin^2 \theta} = \frac{\cos \theta}{\sin \theta} = \cot \theta\)