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