Please solve using the R programming language.

Consider the density f(X) = [1-cos[x-theta]]/(2*Pi) on 0

3.91, 4.85, 2.28, 4.06, 3.70, 4.04. 5.46, 3.53. 2.28, 1.96, 2.53, 3.88, 2.22, 3.47, 4.82, 2.46, 2.99, 2.54, 0.52, and 2.50

We wish to use this data to estimate the parameter theta.

Find the MLE for theta using Newton's method correct to two decimal places. What is the refinement increment h(t)? What was your starting point? How many iterations did it take? What if you changed starting points? Some suggestion are -2.7 and 2.7. Does your method always converge to the correct value of theta? Why or Why not?