(i) Sketch the graphs of \(y = \csc \frac{1}{2}x\) and \(y = \frac{1}{3}x + 1\). The intersection of these graphs in the interval \(0 < x \leq \pi\) indicates a root.

(ii) Calculate the values of the expressions at \(x = 1.4\) and \(x = 1.6\). If there is a sign change, the root lies between these values.

(iii) Rearrange the iterative formula \(x_{n+1} = 2 \sin^{-1} \left( \frac{3}{x_n + 3} \right)\) to show it is equivalent to \(\csc \frac{1}{2}x = \frac{1}{3}x + 1\). This shows convergence to the root.

(iv) Use the iterative formula starting with an initial guess. Calculate successive values to 5 decimal places until they stabilize to 3 decimal places. The final answer is 1.471.