(i)[4]
Find the tangent equation to the curve at the point $(0, 2)$.
(ii)[4]
Show that the $x$-coordinates of the intersection points of the line $y = x + 2$ with the curve satisfy $(x + 2)^2 = x^4 + 4x + 4$. Hence determine these $x$-coordinates.
(iii)[4]
The shaded area in the diagram is turned through $360^\circ$ around the $x$-axis. Find the volume of revolution.