#sin2x+sin3x+sin4x=0.#
#:. (sin4x+sin2x)+sin3x=0.#
#:. 2sin3xcosx+sin3x=0.#
#:. (sin3x)(2cosx+1)=0.#
#:. sin3x=0, or, 2cosx+1=0.#
#:. 3x=kpi, or, cosx=-1/2=cos2pi/3.#
Since, #costheta=cosalpha rArr theta=2kpi+-alpha, k in ZZ,# we have,
# x=kpi/3, or, x=2kpi+-2pi/3, k in ZZ.#