(i)[3]
If $35 + \sec^2 \theta = 12 \tan \theta$, determine the value of $\tan \theta$.
(ii(a))[2]
Hence, by showing the use of a suitable formula, determine the exact value of $\tan(\theta - 45^\circ)$.
(ii(b))[2]
Hence, by showing the use of a suitable formula, determine the exact value of $\tan 2\theta$.