To solve the equation tan(x - π/4) = -1, we can use the inverse tangent function to find the value of x.

Taking the inverse tangent of both sides, we have:

x - π/4 = arctan(-1)

Using the unit circle, we know that the tangent function is negative in the second and fourth quadrants. The angle whose tangent is -1 is π/4 + π, which is 5π/4.

So, x - π/4 = 5π/4

Adding π/4 to both sides, we get:

x = 5π/4 + π/4

x = 6π/4

Simplifying, we have:

x = 3π/2

Therefore, the solution to the equation tan(x - π/4) = -1 is x = 3π/2.

Now, let's solve the equation tan(3x + π/3) = 0.

To find the value of x, we can use the inverse tangent function again.

Taking the inverse tangent of both sides, we have:

3x + π/3 = arctan(0)

The tangent function is equal to 0 at x = 0, π, 2π, 3π, etc. These are the values where the tangent function crosses the x-axis.

So, we have:

3x + π/3 = 0

3x = -π/3

Dividing both sides by 3, we get:

x = -π/9

Therefore, the solution to the equation tan(3x + π/3) = 0 is x = -π/9.