- (a) Prove that
$$\sec 2 A + \tan 2 A \equiv \frac { \cos A + \sin A } { \cos A - \sin A } , \quad A \neq \frac { ( 2 n + 1 ) \pi } { 4 } , n \in \mathbb { Z }$$
(b) Hence solve, for \(0 \leqslant \theta < 2 \pi\),
$$\sec 2 \theta + \tan 2 \theta = \frac { 1 } { 2 }$$
Give your answers to 3 decimal places.