The parametric equations of a curve are x = e^3t , y = t²e^t + 3.
i. Show that y = dy/dx = t(t + 2)/3e^2t

ii. Show that the tangent to the curve at the point (1, 3) is parallel to the x-axis.

iii. Find the exact coordinates of the other point on the curve at which the tangent is parallel to the x-axis.