The diagram shows the curve \(y = \\sin x \\cos 2x\), for \(0 \leq x \leq \\pi\), and a maximum point \(M\), where \(x = a\). The shaded region between the curve and the \(x\)-axis is denoted by \(R\).

(a) Find the value of \(a\) correct to 2 decimal places.

(b) Find the exact area of the region \(R\), giving your answer in simplified form.