Question

[The Icetaker]

Cho \(a,b,c\ne0\); \(a+b\ne c\); \(b+c\ne a\)thỏa mãn \(\frac{a^2+b^2-c^2}{2ab}-\frac{b^2+c^2-a^2}{2bc}+\frac{c^2+a^2-b^2}{2ca}=1.\)

Chứng minh rằng \(a+b+c=0.\)