3.106: Sine equation and shaded area

Solve the equation $\mathrm{sin}\,4x=\dfrac{1}{2}$ for $0\leqslant x\leqslant \dfrac{\pi}{4}$, giving your answers in terms of $\pi$.

The diagram shows parts of the graphs of $y=\mathrm{sin}\,4x$ and $y=\dfrac{1}{2}$. Find the exact area of the shaded region enclosed by the curve and the line.