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?

Enter your answer as the sum of the answers of these questions.

Please take \( \theta\) in degrees.


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