7 The parametric equations of a curve are
$$x = 2 \theta - \sin 2 \theta , \quad y = 2 - \cos 2 \theta$$
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \cot \theta\).
- Find the equation of the tangent to the curve at the point where \(\theta = \frac { 1 } { 4 } \pi\).
- For the part of the curve where \(0 < \theta < 2 \pi\), find the coordinates of the points where the tangent is parallel to the \(x\)-axis.