(a) By sketching a suitable pair of graphs, show that the equation \(\ln x=\operatorname{cosec}\frac12x\) has exactly one root in the interval \(0<x<\pi\).

(b) Verify by calculation that this root lies between \(2.6\) and \(2.9\).

(c) Use the iterative formula \(x_{n+1}=\exp\left(\operatorname{cosec}\frac12x_n\right)\) to determine the root correct to \(3\) decimal places.

Give the result of each iteration to \(5\) decimal places.

\([\exp(x)\text{ is an alternative notation for }e^x.]\)