Fourier series representation of $ x_8(t) = | \cos (2 \pi f_o t) | $

Question

I am trying to compute the Fourier series representation of the following function:

$ x_8(t) = | \cos (2 \pi f_o t) | $

The solution given in the book is the following which is different from my answer:

I am not able to understand whether what I have computed is correct or not. If it is incorrect what is the mistake that I have made? I am enclosing a copy of my answer sheet.

My Solution:

Thanks and regards.