# Rope between inclines?

A rope rests on two platforms which are both inclined at an angle $$\theta$$ (which you are free to pick), as shown. The rope has uniform mass density, and its coefficient of friction with the platforms is 1. The system has left-right symmetry.

What is the largest possible fraction of the rope that does not touch the platforms?

What angle $$\theta$$ allows this maximum value?

Please take $$\theta$$ in degrees.