jmc

Let $r_1,$ $r_2,$ $\dots ,$ $r_7$ be the distinct complex roots of the polynomial $P(x)=x^7-7.$ Let $$K=\prod _{1\le i<j\le 7}(r_i+r_j).$$In other words, $K$ is the product of all numbers of the of the form $r_i+r_j,$ where $i$ and $j$ are integers for which $1\le i<j\le 7.$ Determine $K^2.$