$\begin{array}{l} \cos \left( {\dfrac{\pi }{3} + 3x} \right) + \sin \left( {\dfrac{{5\pi }}{2} + 3x} \right) = 2\\ \Leftrightarrow \cos \left( {\dfrac{\pi }{3} + 3x} \right) + \sin \left( {2\pi + \dfrac{\pi }{2} + 3x} \right) = 2\\ \Leftrightarrow \cos \left( {\dfrac{\pi }{3} + 3x} \right) + \sin \left( {\dfrac{\pi }{2} + 3x} \right) = 2\\ \Leftrightarrow \cos \left( {\dfrac{\pi }{3} + 3x} \right) + \cos \left( {3x} \right) = 2\\ \Leftrightarrow 2\cos \dfrac{\pi }{6}\cos \left( {\dfrac{\pi }{6} + 3x} \right) = 2\\ \Leftrightarrow \cos \left( {\dfrac{\pi }{6} + 3x} \right) = \dfrac{{2\sqrt 3 }}{3} \end{array}$
Vì $\dfrac{2\sqrt 3}{3}>1$ mà $-1\le \cos(\dfrac{\pi}{6}+3x) \le 1$ nên phương trình vô nghiệm
$\Rightarrow S=\emptyset$