A homogeneous \( \operatorname{rod} A B \) of mass \( m \) and length \( l \) leans with its low...

A homogeneous \( \operatorname{rod} A B \) of mass \( m \) and length \( l \) leans with its lower end against the wall and is kept in the inclined position by a string \( D C \) (Fig. 21). The string is tied at point \( C \) to the wall and at point \( D \) to the rod so that \( A D=A B / 3 \). The angles formed by the string and the rod with the wall are \( \alpha \) and \( \beta \) respectively. Find all possible values of the coefficient of friction \( \mu \) between the rod and the wall.
Fig. 21