(Machine shaft displacement)
a. (i) Prove that if an angle θ is measured in radians and the corresponding degree measure is D, then D=π180θ.
b. (ii) A machine shaft turns 75 radians clockwise from its reference position. Convert this rotation to a positive angle between 0∘ and 360∘, expressed in decimal degrees correct to one decimal place.
c. (iii) The shaft then reverses direction and turns 3π radians anticlockwise. Determine the final angular position of the shaft, giving the answer in degrees, minutes and seconds (nearest second).