Friction directions when a block is on the verge of sliding on an inclined plane

[PeroK]

ahh okay. I think I understand that

This sort of thing is definitely worth noting. We have two force equations:

$P_2= \frac{\tan\alpha+\tan\theta}{1-\tan\theta\tan\alpha}$
$P_1=\frac{\tan\theta-\tan\alpha}{\tan\theta\tan\alpha+1}$

The equation for $P_1$ is only valid when $\tan \theta > \tan \alpha = \mu$ and the equation for $P_2$ is only valid when $1 - \tan \theta \tan \alpha > 0$. I.e $\mu < \cot \theta$.

That gives the overall condition that $\mu < \tan \theta, \cot \theta$.