6 The variables \(x\) and \(\theta\) satisfy the differential equation
$$( 3 + \cos 2 \theta ) \frac { \mathrm { d } x } { \mathrm {~d} \theta } = x \sin 2 \theta$$
and it is given that \(x = 3\) when \(\theta = \frac { 1 } { 4 } \pi\).
- Solve the differential equation and obtain an expression for \(x\) in terms of \(\theta\).
- State the least value taken by \(x\).