7. A curve has equation
$$y = \ln ( 1 - \cos 2 x ) , \quad x \in \mathbb { R } , 0 < x < \pi$$
Show that
- \(\frac { \mathrm { d } y } { \mathrm {~d} x } = k \cot x\), where \(k\) is a constant to be found.
Hence find the exact coordinates of the point on the curve where
- \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 \sqrt { 3 }\)