How do you solve Sin(x-4π/3)=2sin(x-π/3)

Question

Math homework. Solve the equation.

Answer 1

sin(x-4π/3) = 2sin(x-π/3)

Or sin(x-π -π/3) = 2sin(x-π/3)

Or -sin(x-π/3) = 2sin(x-π/3) [ using sin(a-π) = -sina ]

Or 3sin(x-π/3) = 0

Or sin(x-π/3) = 0

x-π/3 = nπ

Or x = nπ + π/3