5 A curve has equation \(y = \frac { 2 } { 3 } \ln \left( 1 + 3 \cos ^ { 2 } x \right)\) for \(0 \leqslant x \leqslant \frac { 1 } { 2 } \pi\).
- Express \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(\tan x\).
- Hence find the \(x\)-coordinate of the point on the curve where the gradient is - 1 . Give your answer correct to 3 significant figures.