The diagram shows the points \(O\), \(A\), \(B\), \(C\), \(D\) and \(X\). The position vectors of \(A\), \(B\) and \(C\) relative to \(O\) are \(\overrightarrow{OA}=\mathbf{a}\), \(\overrightarrow{OB}=2\mathbf{b}\) and \(\overrightarrow{OC}=3\mathbf{a}\). The vector \(\overrightarrow{CD}=\mathbf{b}\).

(i) Given that \(\overrightarrow{AX}=\lambda\overrightarrow{AD}\), find \(\overrightarrow{OX}\) in terms of \(\lambda\), \(\mathbf{a}\) and \(\mathbf{b}\).

(ii) Given that \(\overrightarrow{BX}=\mu\overrightarrow{BC}\), find \(\overrightarrow{OX}\) in terms of \(\mu\), \(\mathbf{a}\) and \(\mathbf{b}\).

(iii) Hence find the value of \(\lambda\) and of \(\mu\).

(iv) Find the ratio \(\displaystyle \frac{AX}{XD}\).