7 The variables \(x\) and \(y\) satisfy the differential equation $$\cos 2 x \frac { \mathrm {~d} y } { \mathrm {~d} x } = \frac { 4 \tan 2 x } { \sin ^ { 2 } 3 y }$$ where \(0 \leqslant x < \frac { 1 } { 4 } \pi\). It is given that \(y = 0\) when \(x = \frac { 1 } { 6 } \pi\).
Solve the differential equation to obtain the value of \(x\) when \(y = \frac { 1 } { 6 } \pi\). Give your answer correct to 3 decimal places.