The variables x and θ are related by the differential equation

\(\sin 2θ \frac{dx}{dθ} = (x + 1) \cos 2θ\),

where \(0 < θ < \frac{1}{2}π\). When \(θ = \frac{1}{12}π\), \(x = 0\). Solve the differential equation, obtaining an expression for \(x\) in terms of \(θ\), and simplifying your answer as far as possible.