Use de Moivre's theorem to express \(\cot 7 \theta\) in terms of \(\cot \theta\).

Use the equation \(\cot 7 \theta=0\) to show that the roots of the equation
\(x^{6}-21 x^{4}+35 x^{2}-7=0\)
are \(\cot \left(\frac{1}{14} k \pi\right)\) for \(k=1,3,5,9,11,13\), and deduce that
\(\cot ^{2}\left(\frac{1}{14} \pi\right) \cot ^{2}\left(\frac{3}{14} \pi\right) \cot ^{2}\left(\frac{5}{14} \pi\right)=7\)