How much friction does a ladder need?

A uniform ladder leans on a smooth wall. The shallower it leans, the more friction its foot needs. You will make the program find the least coefficient of friction at every angle, the shallowest safe angle for a floor with $\mu = 0.40$, and the same with a person standing at the top.

The idea. Torques about the foot give the wall's push; friction must balance it. For the ladder alone, $\mu_{\min} = \dfrac{1}{2\tan\theta}$. With a person three times the ladder's weight at the top, $\mu_{\min} = \dfrac{0.5 + 3}{(1 + 3)\tan\theta}$.

Your tasks.

1. Work out mu_alone at every angle in angles.
2. Find the smallest angle at which a floor with $\mu = 0.40$ is enough for the ladder alone.
3. Work out mu_person at every angle, and the smallest safe angle for it.