Two Symmetric Equations

Algebra Level 3

If a,ba, b and cc are non-zero real numbers, that satisfy the equations a2+b2+c2=1 a^2 + b^2 + c^2 = 1 and a(1b+1c)+b(1c+1a)+c(1a+1b)=3a\left(\frac {1}{b} + \frac {1}{c}\right) + b\left(\frac {1}{c} + \frac {1}{a}\right) + c\left( \frac {1}{a} + \frac {1}{b}\right) = -3 , how many possible values are there for a+b+ca + b + c?

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