# Largest fraction of a rope!

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 $$F(\theta) = \sin\theta \cos\theta - \sin^2 \theta$$.

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