(i)[2]
By sketching appropriate graphs, show that the equation $4x^2 - 1 = \cot x$ has a single root in the interval $0 < x < \tfrac{1}{2}\pi$.
(ii)[2]
Use calculation to verify that this root is between $0.6$ and $1$.
(iii)[3]
Apply the iterative formula $x_{n+1} = \tfrac{1}{2}\sqrt{1 + \cot x_n}$ to find the root correct to 2 decimal places. Show each iteration result to 4 decimal places.