$\eqalign{   & 2 - \sin \left( {\frac{{2\pi }}{3}\left( {x - 1} \right)} \right) = 1  \cr   &  - \sin \left( {\frac{{2\pi }}{3}\left( {x - 1} \right)} \right) =  - 1  \cr   & \sin \left( {\frac{{2\pi }}{3}\left( {x - 1} \right)} \right) = 1  \cr   & \frac{{2\pi }}{3}\left( {x - 1} \right) = \frac{1}{2}\pi  + k \cdot 2\pi   \cr   & x - 1 = \frac{3}{4} + k \cdot 3  \cr   & x = 1\frac{3}{4} + k \cdot 3  \cr   & Dus:  \cr   & x = 1\frac{3}{4} \vee x = 4\frac{3}{4} \vee x = 7\frac{3}{4} \cr} $