Fourier transform of triangular function
A triangular function can be generated by convolving two box functions as shown below.



This is where your Step 2 comes from.

The fourier transform of a convolution $g(t) \ast g(t)$ can be calculated by multiplying the fourier transform of $g(t)$ with itself, i.e. $G(\omega)G(\omega)$.

Recall that the Fourier transform of a box function is a Sinc function ($\textrm{sinc}(x) = \frac{\textrm{sin}(x)}{x}$).



Hence, $G(w)$ is some scaled version of a sinc function, and the Fourier transform of the triangular function is $G(w)^2$.