Find the Fourier coefficients of $f(x) = 3 x - 6$, i.e. numbers $a_0$, $b_k$, $c_k$ (note that $b_k$ and $c_k$ may depend on $k$ ) such that $$f(x) = a_0 \frac{1}{\sqrt{2}} + b_1 \sin(x) + c_1 \cos(x) + b_2 \sin(2x) + c_2 \cos(2x) + \ldots.$$
$a_0 =$ ,
$b_k =$ if $k$ is odd, and if $k$ is even,
$c_k =$ if $k$ is odd, and if $k$ is even.