Manian,
The process is fairly simple and straight forward. The total angle of twist of a shaft is obtained by adding algebraically the angles of twist of each component part.
PHI = SUMMATION(TL/GJ)
PHI = ANGLE OF TWIST (in radians)
T = TORQUE
L = LENGTH OF SHAFT
G = MODULUS OF RIGIDITY
J = POLOR MOMENT OF INERTIA (pi*r^4 /2 for round shaft)