(a)[4]
Show that, from your working, $\tan a = \frac{1}{2}a$.
(b)[2]
Verify by calculation that $a$ is between $2$ and $2.5$.
(c)[2]
Show that, if a sequence of values in the interval $0 < x < \pi$ is generated by the iterative formula $x_{n+1} = \pi - \tan^{-1}\left(\frac{1}{2}x_n\right)$ and it converges, then its limit is $a$, the root of the equation in part (a).
(d)[3]
Use the iterative process given in part (c) to find $a$ correct to 2 decimal places. Give each iteration to 4 decimal places.