(a)[2]
Using a pair of suitable sketches, show that the equation $|x - 2| = 2\sin\tfrac{1}{2}x$ has only one root in the interval $0 < x < \pi$.
(b)[2]
Show by calculation that this root is between $1$ and $1.5$.
(c)[3]
Use the iterative formula $x_{n+1} = 2 - 2\sin\tfrac{1}{2}x_n$ with an initial value of $1.03$ to find the root correct to $2$ decimal places. Give each iteration to $4$ decimal places.