The function g(x)=sin2x is considered on the interval [0,π]. Work through the following tasks.
a. (i) Determine the average rate of change of g on [0,π].
b. (ii) Solve for all real numbers c in (0,π) that satisfy g′(c) equal to the average rate calculated in part (i).
c. (iii) State the total number of distinct values of c obtained and provide a brief justification for your count.