An ant on a triangle

An ant is on the vertex of a triangle. It can move 'left' with probability of \(\frac{1}{2}\) and 'right' with probability of \(\frac{1}{2}\). Note that, the meaning of "moving left or right" is on the corresponding triangle's sides. The expected number of moves till it first reaches its starting point is \({\dfrac{a}{b}}\), where \({a}\) and \({b}\) are positive coprime integers. Calculate \({a+b}\).

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