6. The curve \(C\) has parametric equations
$$x = \theta - \tanh \theta , \quad y = \operatorname { sech } \theta , \quad 0 \leqslant \theta \leqslant \ln 3$$
- Find
- \(\frac { \mathrm { d } x } { \mathrm {~d} \theta }\)
- \(\frac { \mathrm { d } y } { \mathrm {~d} \theta }\)
The curve \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.
- Find the exact area of the curved surface formed, giving your answer as a multiple of \(\pi\).