From Förberedande kurs i matematik 1

Using the unit circle shows that the equation \displaystyle \text{cos 3}x=-\frac{1}{\sqrt{2}} has two solutions for \displaystyle 0\le \text{3}x\le \text{2}\pi ,

\displaystyle 3x=\frac{\pi }{2}+\frac{\pi }{4}=\frac{3\pi }{4} and \displaystyle 3x=\pi +\frac{\pi }{4}=\frac{5\pi }{4}

We obtain the other solutions by adding multiples of \displaystyle 2\pi ,

\displaystyle 3x=\frac{3\pi }{4}+2n\pi and \displaystyle 3x=\frac{5\pi }{4}+2n\pi

i.e.

\displaystyle x=\frac{\pi }{4}+\frac{2}{3}n\pi and \displaystyle x=\frac{5\pi }{12}+\frac{2}{3}n\pi

where \displaystyle n is an arbitrary integer.