The parametric equations of a curve are \(x = \frac{1}{\cos t}\), \(y = \ln \tan t\), where \(0 < t < \frac{1}{2}\pi\).

(a) Show that \(\frac{dy}{dx} = \frac{\cos t}{\sin^2 t}\).

(b) Find the equation of the tangent to the curve at the point where \(y = 0\).