The variables x and θ satisfy the differential equation \(\frac{dx}{dθ} = (x + 2) \sin^2 2θ\), and it is given that \(x = 0\) when \(θ = 0\). Solve the differential equation and calculate the value of x when \(θ = \frac{1}{4}π\), giving your answer correct to 3 significant figures.