3. A curve \(C\) has parametric equations
$$x = \sqrt { 3 } \tan \theta , \quad y = \sec ^ { 2 } \theta , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 3 }$$
The cartesian equation of \(C\) is
$$y = \mathrm { f } ( x ) , \quad 0 \leqslant x \leqslant k , \quad \text { where } k \text { is a constant }$$
- State the value of \(k\).
- Find \(\mathrm { f } ( x )\) in its simplest form.
- Hence, or otherwise, find the gradient of the curve at the point where \(\theta = \frac { \pi } { 6 }\)