By sketching a suitable pair of graphs, show that there is only one value of \(x\) in the interval \(0 < x < \frac { 1 } { 2 } \pi\) that is a root of the equation
$$\cot x = x$$
Verify by calculation that this root lies between 0.8 and 0.9 radians.
Show that this value of \(x\) is also a root of the equation
$$x = \tan ^ { - 1 } \left( \frac { 1 } { x } \right)$$
Use the iterative formula
$$x _ { n + 1 } = \tan ^ { - 1 } \left( \frac { 1 } { x _ { n } } \right)$$
to determine this root correct to 2 decimal places, showing the result of each iteration.