\[ \Leftrightarrow 4\frac{{(1 + c{\rm{os2x)}}^{\rm{2}} }}{4} - \cos 2x - \frac{1}{2}(\cos ^2 2x - \sin ^2 2x) + \cos \frac{{3x}}{4} = \frac{7}{2}\\]
\[ \Leftrightarrow 1 + \cos 2x + \cos \frac{{3x}}{4} + \frac{1}{2} = \frac{7}{2}\\]
\[ \Leftrightarrow \frac{3}{2} + \cos 2x + \cos \frac{{3x}}{4} = \frac{7}{2}\\]
\[ \left\{ \begin{array}{l} \cos 2x = 1 \\ \cos \frac{{3x}}{4} = 1 \\ \end{array} \right.\\]