4 The matrix \(\mathbf { M }\) is given by \(\mathbf { M } = \left( \begin{array} { c c } \cos \theta & - \sin \theta
\sin \theta & \cos \theta \end{array} \right) \left( \begin{array} { l l } 3 & 0
0 & 1 \end{array} \right)\).

1. The matrix \(\mathbf { M }\) represents a sequence of two geometrical transformations. State the type of each transformation, and make clear the order in which they are applied.
2. Find the values of \(\theta\), for \(0 \leqslant \theta \leqslant \pi\), for which the transformation represented by \(\mathbf { M }\) has exactly one invariant line through the origin, giving your answers in terms of \(\pi\).