To simplify this expression, we can use the trigonometric identity:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

Using this identity, we can rewrite the expression as:

sin(π + 3/4x) - sin(3π/2 - 3/4x) = 0
(sin(π)cos(3/4x) + cos(π)sin(3/4x)) - (sin(3π/2)cos(-3/4x) + cos(3π/2)sin(-3/4x)) = 0
(0cos(3/4x) + (-1)sin(3/4x)) - (-1cos(3/4x) + 0sin(-3/4x)) = 0
-sin(3/4x) + cos(3/4x) = 0

Now we can rewrite the expression as:

cos(3/4x) = sin(3/4x)

This implies:

tan(3/4x) = 1

Therefore, the general solution to this equation is:

3/4x = π/4 + nπ, where n is an integer

x = π/3 + 4nπ/3, where n is an integer.