6 The variables \(x\) and \(y\) satisfy the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = 4 \cos ^ { 2 } y \tan x ,$$ for \(0 \leqslant x < \frac { 1 } { 2 } \pi\), and \(x = 0\) when \(y = \frac { 1 } { 4 } \pi\). Solve this differential equation and find the value of \(x\) when \(y = \frac { 1 } { 3 } \pi\).