Complex Complex Numbers !!

Algebra Level 2

Z1=Z2=Z3=1Z1+1Z2+1Z3=1|Z_{1}| = |Z_{2}| = |Z_{3}| = \Bigg|\dfrac{1}{Z_1} + \dfrac{1}{Z_{2}} + \dfrac{1}{Z_{3}} \Bigg| = 1

If Z1,Z2,Z3Z_{1} , Z_{2} , Z_{3} are complex numbers in the argand plane satisfying the above equalities, find the value of:

Z1+Z2+Z3= ? \bigg|Z_{1} + Z_{2} + Z_{3} \bigg| = \ ?

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