Euler E703: An easy method for finding series in sines or cosines of multiple angles, with extensive use throughout the theory of astronomy | English translation | OMH v1.0

English translation of Leonhard Euler's E703, An easy method for finding series in sines or cosines of multiple angles, with extensive use throughout the theory of astronomy. AI use and review status: OpenAI tools assisted with the translation and LaTeX. Version 1.0 is a machine draft with limited scholarly human inspection. Version 2.0 is reserved for a fully reviewed edition. Sources: Official Euler Archive record E703, https://scholarlycommons.pacific.edu/euler-works/703/; Nova Acta Academiae Scientiarum Imperialis Petropolitanae, volume XI, history through 1793, Petropoli: Typis Academiae Scientiarum, 1798, pp. 94–113, https://archive.org/details/novaactaacademia11petr; Natural History Museum Library, London, Biodiversity Heritage Library item 113775, https://www.biodiversitylibrary.org/item/113775.