From Förberedande kurs i matematik 1

We see directly that \displaystyle x=\frac{\pi }{5} is a solution to the equation, and using the unit circle we can also draw the conclusion that \displaystyle x=\pi -\frac{\pi }{5}=\frac{4\pi }{5} is the only other solution between \displaystyle 0 and \displaystyle \text{2}\pi .

We obtain all solutions to the equation when we add integer multiples of \displaystyle \text{2}\pi ,

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

where \displaystyle n is an arbitrary integer.