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Create Pattern along spiral path

Experimenter
Experimenter

I need to create a pattern along a spiral that will iterate a feature every 137.5 degrees along the path. Since the arc length is continuously changing as the spiral "tightens" I'm not sure how to correctly input a formula that will vary the arc length as the path continues. How can I iterate this feature along the path to get a consistent angle around the spiral with respect the the previous iteration?