By sketching a suitable pair of graphs, show that the equation
$$\cot x = 2 - \cos x$$
has one root in the interval \(0 < x \leqslant \frac { 1 } { 2 } \pi\).
Show by calculation that this root lies between 0.6 and 0.8 .
Use the iterative formula \(x _ { n + 1 } = \tan ^ { - 1 } \left( \frac { 1 } { 2 - \cos x _ { n } } \right)\) to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.