A circle of radius 1 is drawn in the plane. Four non-overlapping circles each of radius 1, are drawn (externally) tangential to the original circle. An angle ã is chosen uniformly at random in the interval [0,2ð). The probability that a half ray drawn from the centre of the original circle at an angle of ã intersects one of the other four circles can be expressed as ab, where a and b are coprime positive integers. What is the value of a+b?
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