The diagram shows part of the curve \(y=a+4\cos bx\), where \(a\) and \(b\) are positive constants. The curve meets the \(y\)-axis at the point \((0,6)\) and the \(x\)-axis at the point \(\left(\dfrac{\pi}{6},0\right)\). The curve meets the \(x\)-axis again at the point \(P\) and has a minimum at the point \(M\).

(i) Find the value of \(a\) and of \(b\).

Using your values of \(a\) and \(b\), find

(ii) the exact coordinates of \(P\),

(iii) the exact coordinates of \(M\).