$$\eqalign{
& 2{\sin ^2}\left( {x - {\pi \over 4}} \right) + \sqrt 3 \cos 2x - 1 = 0 \cr
& \Leftrightarrow 1 - \cos \left( {2x - {\pi \over 2}} \right) + \sqrt 3 \cos 2x - 1 = 0 \cr
& \Leftrightarrow - \cos \left( {{\pi \over 2} - 2x} \right) + \sqrt 3 \cos 2x = 0 \cr
& \Leftrightarrow - \sin 2x + \sqrt 3 \cos 2x = 0 \cr
& \Leftrightarrow \sin 2x = \sqrt 3 \cos 2x \cr
& \Leftrightarrow \tan 2x = \sqrt 3 \cr
& \Leftrightarrow 2x = {\pi \over 3} + k\pi \Leftrightarrow x = {\pi \over 6} + {{k\pi } \over 2}\,\,\left( {k \in Z} \right) \cr} $$
