The numbers \(\cot (\theta - \alpha),3 \cot \theta,\cot (\theta + \alpha)\) form an arithmetic progression, in that order. Assuming \(\sin \alpha \neq 0, \), compute \(\frac{\sin^2 \theta}{\sin^2 \alpha}.\)
I've tried to use the fact that \(d = 3 \cot \theta-\cot (\theta - \alpha)=\cot (\theta + \alpha)-3 \cot \theta\), but I don't know how to continue.
