Mind Boggling Bullseye Part 2

The dartboard in the diagram consists of an infinite number of concentric circles. Each successively smaller circle has \(\frac{3}{4}\) the radius of the preceding, larger circle.

A dart is thrown somewhere on the dartboard (striking uniformly at random over the entire area of the dartboard).

To 2 decimal places, what is the probability it strikes black? Assume the point of the dart is one-dimensional.

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