(a)[3]
Show that the $x$-coordinate of $M$ satisfies the equation $x = \sqrt[3]{1.5x^2 \cot 2x}$.
(b)[2]
Apply the equation in part (a) and, by calculation, show that the $x$-coordinate of $M$ lies between $0.59$ and $0.60$.
(c)[3]
Use iteration, based on the equation in part (a), to determine the $x$-coordinate of $M$ correct to $3$ significant figures. Give each iteration result to $5$ significant figures.