$(35$ Points$)$ The steel $(G=10,800$ksi $)$ shaft is made from two segments: AC has a diameter of $0\mathrm{.}5$ in and CB has a diameter of $1$ in $.$ If the shaft is fixed at both ends and subjected to the torque shown, determine the following:

$[$a$]$ maximum shear stress in the shaft

$[$b$]$ angle of twist at point $D($provide answer in degrees$)$