(a)[4]
Show that $\tan 2a = -4a$.
(b)[2]
Show by calculation that $0.9 \le a \le 0.95$.
(c)[2]
Show that if a sequence of values produced by the iterative formula $x_{n+1} = \tfrac{1}{2}\left(\pi - \tan^{-1}(4x_n)\right)$ converges, then it converges to $a$.
(d)[3]
Use the iterative formula from part (c) to find $a$ correct to 4 decimal places, and write each iterate to 6 decimal places.