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Let a,b,ca, b, ca,b,c be 3 complex numbers such that ∣a∣=∣b∣=∣c∣=1|a| = |b| = |c| = 1∣a∣=∣b∣=∣c∣=1 and a2bc+b2ac+c2ab+1=0\dfrac{a^2}{bc}+ \dfrac{b^2}{ac} + \dfrac{c^2}{ab} + 1 = 0bca2+acb2+abc2+1=0 . If ∣a+b+c∣|a + b + c|∣a+b+c∣ can take values that equal ppp and qqq, then find the value of p+qp+qp+q .
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