3. The curve \(C\) has parametric equations
$$x = 3 + 2 \sin t \quad y = \frac { 6 } { 7 + \cos 2 t } \quad - \frac { \pi } { 2 } \leqslant t \leqslant \frac { \pi } { 2 }$$
- Show that \(C\) has Cartesian equation
$$y = \frac { 12 } { ( 7 - x ) ( 1 + x ) } \quad p \leqslant x \leqslant q$$
where \(p\) and \(q\) are constants to be found.
- Hence, find a Cartesian equation for \(C\) in the form
$$y = \frac { a } { x + b } + \frac { c } { x + d } \quad p \leqslant x \leqslant q$$
where \(a , b , c\) and \(d\) are constants.