- (i) Using the identity for \(\tan ( A \pm B )\), solve, for \(- 90 ^ { \circ } < x < 90 ^ { \circ }\),
$$\frac { \tan 2 x + \tan 32 ^ { \circ } } { 1 - \tan 2 x \tan 32 ^ { \circ } } = 5$$
Give your answers, in degrees, to 2 decimal places.
(ii) (a) Using the identity for \(\tan ( A \pm B )\), show that
$$\tan \left( 3 \theta - 45 ^ { \circ } \right) \equiv \frac { \tan 3 \theta - 1 } { 1 + \tan 3 \theta } , \quad \theta \neq ( 60 n + 45 ) ^ { \circ } , n \in \mathbb { Z }$$
(b) Hence solve, for \(0 < \theta < 180 ^ { \circ }\),
$$( 1 + \tan 3 \theta ) \tan \left( \theta + 28 ^ { \circ } \right) = \tan 3 \theta - 1$$