\(sina-cosa=-\sqrt{2}\)
\(\Leftrightarrow sina.\frac{\sqrt{2}}{2}-cosa.\frac{\sqrt{2}}{2}=-1\)
\(\Leftrightarrow sina.cos\frac{\pi}{4}-cosa.sin\frac{\pi}{4}=-1\)
\(\Leftrightarrow sin\left(a-\frac{\pi}{4}\right)=-1\)
\(\Rightarrow a-\frac{\pi}{4}=-\frac{\pi}{2}\Rightarrow a=-\frac{\pi}{4}\)