For sin3x+sinx=0,\displaystyle {\sin{{3}}}{x}+{\sin{{x}}}={0}, use a sum-to-product formula to simplify the equation and then find all solutions of the equation in the interval [0,π).\displaystyle {\left[{0},\pi\right)}.
The answer is x1=\displaystyle {x}_{{1}}=   and x2=\displaystyle {x}_{{2}}=   with x1<x2\displaystyle {x}_{{1}}\lt{x}_{{2}}.