The value of \(\mathop \smallint \nolimits_0^{2{\rm{\pi }}} \left[ {{\rm{sin}}2{\rm{x}}\left( {1 + {\rm{cos}}3{\rm{x}}} \right)} \right]{\rm{dx}}\), where [t] denotes the greatest integer function, is:

• A. π
• B. -π
• C. -2π
• D. 2π