The equation \(x^{3}+2 x^{2}+x+7=0\) has roots \(\alpha, \beta, \gamma\).
(i) Use the relation \(x^{2}=-7 y\) to show that the equation
\(49 y^{3}+14 y^{2}-27 y+7=0\)
has roots \(\frac{\alpha}{\beta \gamma}, \frac{\beta}{\gamma \alpha}, \frac{\gamma}{\alpha \beta}\).

(ii) Show that \(\frac{\alpha^{2}}{\beta^{2} \gamma^{2}}+\frac{\beta^{2}}{\gamma^{2} \alpha^{2}}+\frac{\gamma^{2}}{\alpha^{2} \beta^{2}}=\frac{58}{49}\).

(iii) Find the exact value of \(\frac{\alpha^{3}}{\beta^{3} \gamma^{3}}+\frac{\beta^{3}}{\gamma^{3} \alpha^{3}}+\frac{\gamma^{3}}{\alpha^{3} \beta^{3}}\).