In a lever$-$pendulum mechanism, the dead position angles of the arm and the pendulum are $150\backslash$deg and $60\backslash$deg $,$ respectively. Let the fixed link length be unit and the ratio of the length of the connecting rod to the length of the arm be $2.$ In this case, what are the lengths of the limbs in the mechanism? Find the smallest and largest values of the coupling angle formed between the connecting rod and the pendulum in the mechanism you found.