A curve has equation \(y=x\sin2x\).

(a) Find \(\frac{\mathrm dy}{\mathrm dx}\).

(b) Find the equation of the tangent to the curve at \(x=\frac\pi4\).

(c) Use your answer to part (a) to find the exact value of

\(\displaystyle \int_0^{\pi/6}2x\cos2x\,\mathrm dx.\)