The equation \(\cot x = 1 - x\) has one root in the interval \(0 < x < \pi\), denoted by \(\alpha\).

(i) Show by calculation that \(\alpha\) is greater than 2.5.

(ii) Show that, if a sequence of values in the interval \(0 < x < \pi\) given by the iterative formula \(x_{n+1} = \pi + \arctan \left( \frac{1}{1-x_n} \right)\) converges, then it converges to \(\alpha\).

(iii) Use this iterative formula to determine \(\alpha\) correct to 3 decimal places. Give the result of each iteration to 5 decimal places.