Doubt on complex number

Let \color{brown}a,b,c be \color{brown}3 complex number such that \color{brown}|a|=|b|=|c|=1 and \color{brown}\displaystyle \frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}+1=0. Then possible values of \color{brown}|a+b+c| is /are.

1,-1,-1satisfy so 1 would be possible

i,I,-i)( i-i,-i) also satisfied

(w^2,w,-1)and (w^2,1+_7i/2,w) so 2 and 5/✓2 also possible