We can solve this equation by finding the values of x that satisfy the equation.

First, let's simplify the equation:

sin(x/2 - π/8)*(tan(x) - 1) = 0
sin(x/2 - π/8) = 0 or tan(x) - 1 = 0

Now, let's solve each part separately:

sin(x/2 - π/8) = 0
x/2 - π/8 = nπ, where n is an integer
x/2 = nπ + π/8
x = 2nπ + π/4

tan(x) - 1 = 0
tan(x) = 1
x = π/4

Therefore, the solutions to the equation are x = 2nπ + π/4 and x = π/4, where n is an integer.