To solve the equation sin(x + π/4) = 0, we need to find the values of x that satisfy this equation.

The sine function has a period of 2π, which means that sin(x) = sin(x + 2π) for any value of x. Therefore, we can write the equation as sin(x + π/4 + 2π) = 0.

To find the values of x that satisfy this equation, we need to find the values of x + π/4 + 2π that make sin(x + π/4 + 2π) = 0.

Since sin(0) = 0, we can set x + π/4 + 2π = 0, which gives us x = -π/4 - 2π.

Therefore, the solution to the equation sin(x + π/4) = 0 is x = -π/4 - 2π + 2πn, where n is an integer.