A curve has parametric equations
\(x=2 \theta-\sin 2 \theta, \quad y=1-\cos 2 \theta, \quad \text { for }-3 \pi \leqslant \theta \leqslant 3 \pi\)

Show that
\(\frac{\mathrm{d} y}{\mathrm{~d} x}=\cot \theta\)
except for certain values of \(\theta\), which should be stated.

Find the value of \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) when \(\theta=\frac{1}{4} \pi\).