A certain machine requires a torque of \((500+50 \sin 2 \theta) \mathrm{kN} \cdot \mathrm{m}\) to drive it, where \(\theta\) is the angle of rotation of shaft measured from certain datum. The machine is directly coupled to an engine which produces a torque \((500+50 \sin \theta) \mathrm{kN} \cdot \mathrm{m}\) in a cycle. How many times the value of torque of machine and engine will be identical?

(a) 1

(b) 2

(c) 4

(d) 8 .