Straight up unfair

Level pending

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

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