(a(i))[2]
By drawing an appropriate pair of graphs, show that the equation $\cot x = 4x - 2$, where $x$ is in radians, has only one root for $0 \le x \le \tfrac{1}{2}\pi$.
(a(ii))[2]
Check by calculation that this root is between $x = 0.7$ and $x = 0.9$.
(a(iii))[1]
Show that this root also satisfies the equation $x = \dfrac{1 + 2\tan x}{4\tan x}$.
(a(iv))[3]
Apply the iterative formula $x_{n+1} = \dfrac{1 + 2\tan x_n}{4\tan x_n}$ to find this root correct to $2$ decimal places. Record every iteration to $4$ decimal places.