In the triangle \(OAB\), \(\overrightarrow{OA}=\mathbf a\) and \(\overrightarrow{OB}=\mathbf b\).

The straight line \(XYZ\) is such that:

\(\overrightarrow{OX}=\frac45\mathbf b\)

\(\overrightarrow{AY}=\frac13\overrightarrow{AB}\)

\(\overrightarrow{AZ}=\mu\mathbf a\), where \(\mu\) is a constant

\(\overrightarrow{YZ}=\lambda\overrightarrow{XY}\), where \(\lambda\) is a constant.

(a) Show that \(\overrightarrow{XY}=\frac23\mathbf a-\frac7{15}\mathbf b\).

(b) Find \(\overrightarrow{YZ}\) in terms of \(\lambda\), \(\mathbf a\) and \(\mathbf b\).

(c) Find \(\overrightarrow{YZ}\) in terms of \(\mu\), \(\mathbf a\) and \(\mathbf b\).

(d) Hence find the values of \(\lambda\) and \(\mu\).