A heavy metal bar AB rests with its lower end A on a rough horizontal floor having coefficient of friction $\mu_F$ and the other end b on a rough vertical wall having coefficient of friction $\mu_w$. If the center of gravity of the bar is at distance a and b from the ends A and B respectively, show that at impeding motion, the inclination of three bar with the horizontal will be:

$$ \theta = tan^{-1}(\frac{1}{\mu_F}. \frac{a - b \mu_F \mu_w}{a+b} )$$