Straight up unfair

You are bored one day and decide to keep flipping an unfair coin until it lands on tails. It has a 60%60\% chance of landing on heads. If you get tails on the NthN^\text{th} flip, the probability that NN is an integer multiple of 3 can be expressed as ab\frac{a}{b}, where aa and bb are coprime positive integers. Find a+b.a+b.

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