6 The variables \(x\) and \(\theta\) satisfy the differential equation $$\sin \frac { 1 } { 2 } \theta \frac { d x } { d \theta } = ( x + 2 ) \cos \frac { 1 } { 2 } \theta$$ for \(0 < \theta < \pi\). It is given that \(x = 1\) when \(\theta = \frac { 1 } { 3 } \pi\). Solve the differential equation and obtain an expression for \(x\) in terms of \(\cos \theta\).