$ 4sin^2 x - 4sin x + 1 - 4sin^2 x - 4sin x - 1 = 4\sqrt{2} $
$ - 4sin x - 4sin x = 4\sqrt{2} $
$ -8sin x = 4\sqrt{2} $
$ sin x = - \frac {\sqrt{2}}{2} $
$ x = -\frac{\pi}{4} + 2k\pi \; \lor \; x = \frac{5\pi}{4} + 2k\pi; \qquad k \in \mathbb{Z} $