The equation to solve is \( \csc(2x) = -\sqrt{2} \). This can be transformed into:
\[ \csc(2x) = \frac{1}{\sin(2x)} \Rightarrow \sin(2x) = -\frac{1}{\sqrt{2}} \]
The equation to solve is \( \csc(2x) = \sqrt{2} \). This can be transformed into:
\[ \csc(2x) = \frac{1}{\sin(2x)} \Rightarrow \sin(2x) = \frac{1}{\sqrt{2}} \]
