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Liars, Liars...?

In the land of Brainopia, there are three races of people: Mikkos, who tell the truth all the time, Kikkos, who always tell lies, and Zikkos, who tell alternate false and true statements, in which the order is not known (i.e. true, false, true or false, true, false). When interviewing three Brainopians, a foreigner received the following statements:

Person 1:
I am a Mikko.

Person 2:
I am a Kikko.

Person 3:
a. They are both lying.
b. I am a Zikko.

Can you help the very confused foreigner determine who is who, assuming each person represents a different race?

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