(i)[2]
By sketching suitable graphs, show that the equation $4x^2 - 1 = \cot x$ has just one root in the interval $0 < x < \frac{1}{2}\pi$.
(ii)[2]
Confirm by calculation that this root is located between $0.6$ and $1$.
(iii)[3]
Use the iterative formula $x_{n+1} = \frac{1}{2}\sqrt{(1 + \cot x_n)}$ to find the root correct to $2$ decimal places. Write the outcome of each iteration to $4$ decimal places.