The sequence of values given by the iterative formula \(x_{n+1} = \frac{2}{3} \left( x_n + \frac{1}{x_n^2} \right)\), with initial value \(x_1 = 1\), converges to \(\alpha\).

(i) Use this formula to find \(\alpha\) correct to 2 decimal places, showing the result of each iteration.

(ii) State an equation satisfied by \(\alpha\), and hence find the exact value of \(\alpha\).