4. (a) Prove that
$$\frac { 1 - \cos 2 x } { \sin 2 x } \equiv \tan x , \quad x \neq \frac { n \pi } { 2 }$$
(b) Hence solve, for \(0 \leqslant \theta < 2 \pi\),
$$3 \sec ^ { 2 } \theta - 7 = \frac { 1 - \cos 2 \theta } { \sin 2 \theta }$$
Give your answers in radians to 3 decimal places, as appropriate.
(Solutions based entirely on graphical or numerical methods are not acceptable.)