The variables \(x\) and \(y\) satisfy the equation \(y^2=k\frac{x-2}{x+2}\), where \(k\) is a constant.

(a) Show that \(\frac{dy}{dx}=\frac{2y}{x^2-4}\).

(b) Given that \(k=5\), find the angle between the tangents to the curve when \(x=3\).

Give your answer in the form \(a\tan^{-1}\left(\frac bc\right)\), where \(a\), \(b\) and \(c\) are integers.