6 It is given that the angle \(\theta\) satisfies the equation \(\sin \left( 2 \theta + \frac { 1 } { 4 } \pi \right) = 3 \cos \left( 2 \theta + \frac { 1 } { 4 } \pi \right)\).
- Show that \(\tan 2 \theta = \frac { 1 } { 2 }\).
- Hence find, in surd form, the exact value of \(\tan \theta\), given that \(\theta\) is an obtuse angle.