A curve is given by the parametric equations $x = e^{3t},\ y = t^2e^t + 3$.
(i)[4]
Show that, for this curve, $\displaystyle \frac{dy}{dx} = \frac{t(t + 2)}{3e^{2t}}$.
(ii)[2]
Show that the tangent to the curve at the point $(1, 3)$ is parallel to the $x$-axis.
(iii)[2]
Find the exact coordinates of the other point on the curve where the tangent is parallel to the $x$-axis.
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