To solve this equation, we will use the identity sin(3x) = 3sin(x) - 4sin^3(x) to simplify the left side of the equation.

sin(3x) + sin(x) = 4sin^3(x)

Using the identity sin(3x) = 3sin(x) - 4sin^3(x), we can rewrite the equation as:

3sin(x) - 4sin^3(x) + sin(x) = 4sin^3(x)

Combining like terms on the left side, we get:

4sin(x) - 4sin^3(x) = 4sin^3(x)

Rearranging the equation, we get:

4sin(x) = 8sin^3(x)

Dividing both sides by 4sin(x), we get:

1 = 2sin^2(x)

Taking the square root of both sides, we get:

√1 = √2sin^2(x)

1 = √2sin(x)

Finally, dividing by √2, we get:

sin(x) = 1/√2

Therefore, the solution to the equation sin(3x) + sin(x) = 4sin^3(x) is sin(x) = 1/√2.