Answer:
[tex]arcsin(\frac{R\mu}{(R+l)\sqrt{\mu^2+1}})[/tex]
Explanation:
By the Law of Sines,
[tex]sin \theta = \frac{sin \phi R}{ l + R}[/tex]
From Newton's Law,
[tex]mg = N\sqrt{\mu^2+1}[/tex]
And the last equation again from Newton's Law,
[tex]\mu N = mgsin\phi[/tex]
Then if we collect all equations together,
[tex]\mu N = mgsin\phi = N\sqrt{\mu^2+1}sin\phi\\[/tex]
[tex]sin\theta = \frac{\mu R}{ (l + R)\sqrt{\mu^2+1}}[/tex]
Thus,
[tex]\theta = arcsin(\frac{R\mu}{(R+l)\sqrt{\mu^2+1}})[/tex]
