[tex]sin a + sin b = 2 sin (\frac{a+b}{2}) cos(\frac{a-b}{2})[/tex]
Let a = 3x, b = x
[tex]=\ \textgreater \ 2 sin(2x) cos(x) = 0[/tex]
Set each factor equal to 0:
[tex]sin (2x) = 0 \\ 2x = 0, \pi \\ x = 0, \frac{ \pi }{2}[/tex]
[tex]cos (x) = 0 \\ x = \frac{ \pi }{2}, \frac{3 \pi }{2} [/tex]
Final solution:
[tex]x = 0, \frac{ \pi }{2}, \frac{ 3\pi }{2}[/tex]
