The matrix M is given by \(\mathbf{M} = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix} \begin{pmatrix} 3 & 0 \\ 0 & 1 \end{pmatrix}\).

(a) The matrix 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]

(b) Find the values of \(\theta\), for \(0 \leq \theta \leq \pi\), for which the transformation represented by M has exactly one invariant line through the origin, giving your answers in terms of \(\pi\). [9]