7 The variables \(x\) and \(t\) satisfy the differential equation
$$\mathrm { e } ^ { 3 t } \frac { \mathrm {~d} x } { \mathrm {~d} t } = \cos ^ { 2 } 2 x$$
for \(t \geqslant 0\). It is given that \(x = 0\) when \(t = 0\).
- Solve the differential equation and obtain an expression for \(x\) in terms of \(t\).
- State what happens to the value of \(x\) when \(t\) tends to infinity.