The diagram shows a quadrilateral \(OABC\). The point \(D\) lies on \(OB\) such that \(\overrightarrow{OD}=2\overrightarrow{DB}\) and \(\overrightarrow{AD}=m\overrightarrow{AC}\), where \(m\) is a scalar quantity.

\(\overrightarrow{OA}=\mathbf a,\qquad \overrightarrow{OB}=\mathbf b,\qquad \overrightarrow{OC}=\mathbf c.\)

(i) Find \(\overrightarrow{AD}\) in terms of \(m\), \(\mathbf a\) and \(\mathbf c\).

(ii) Find \(\overrightarrow{AD}\) in terms of \(\mathbf a\) and \(\mathbf b\).

(iii) Given that \(15\mathbf a=16\mathbf b-9\mathbf c\), find the value of \(m\).