Indefinite Integrals

If $\int {{{d\theta } \over {{{\cos }^2}\theta \left( {\tan 2\theta + \sec 2\theta } \right)}}} = \lambda \tan \theta + 2{\log _e}\left| {f\left( \theta \right)} \right| + C$ where C is a constant of integration, then the ordered pair ($\lambda$, ƒ($\theta$)) is equal to :