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If a^(2)+b^(2)+c^(2)+ab+bc+ca le 0 AA a,...

If `a^(2)+b^(2)+c^(2)+ab+bc+ca le 0 AA a,b,c in R`, then value of the determinant `|{:((a+b+2)^(2),a^(2)+b^(2),1),(1,(b+c+2)^(2),b^(2)+c^(2)),(c^(2)+a^(2),1,(c+a+2)^(2)):}|` equals

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