Determine the fourier seriers for the periodic function

Question

I need help to determine the Fourier series for the periodic function of:

$$f(x)= \left\{\begin{array}{ll}-2 &:&-\pi< x<-\pi/2\\ 2 &:&-π/2<x<π/2\\ \\-2 &:& π/2<x<π \end{array}\right..$$

Find the values of $a$'s and $b$'s and solve the equation.

Here is an image of the function.