Вычислите интеграл \(\large{{\int\limits_0^{\large\frac{2{\pi}}{3}}}(\sin{\large\frac{x}{4}}+{\cos{\large\frac{x}{4}}})^2dx.}\)

• \(\large\dfrac{2{\pi}+3}{3}\)
• \(\large\dfrac{{\pi}}{3}\)
• \(1\)
• \(\large{\dfrac{{\pi}}{3}-1}\)