\(sin4x+\sqrt{3}cos4x=2\)
\(\Leftrightarrow\dfrac{1}{2}sin4x+\dfrac{\sqrt{3}}{2}cos4x=1\)
\(\Leftrightarrow sin\left(4x+\dfrac{\pi}{3}\right)=1\)
\(\Leftrightarrow4x+\dfrac{\pi}{3}=k2\pi\)
\(\Leftrightarrow x=-\dfrac{\pi}{12}+\dfrac{k\pi}{2}\)
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