A rope rests on two platforms which are both inclined at an angle \(\theta\), as shown. The rope has uniform mass density \(\lambda\), and its coefficient of friction with the platforms is \(\mu=1\). The system has left-right symmetry.
What is the largest possible fraction of the rope that does not touch the platforms?
With \(F(\theta) = \sin\theta \cos\theta - \sin^2 \theta\).