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Young and active stars generally have regular, almost sinusoidal, patterns of variability attributed to their rotation, while the majority of older and less active stars, including the Sun, have more complex and non-regular light-curves which do not have clear rotational-modulation signals. Consequently, the rotation periods have been successfully determined only for a small fraction of the Sun-like stars observed by transit-based planet-hunting missions, such as CoRoT, Kepler, and TESS. This suggests that only a small fraction of such systems have been properly identified as solar-like analogs. We apply a new method for determining rotation periods of low-activity stars, like the Sun. The method is based on calculating the gradient of the power spectrum (GPS) of stellar brightness variations and identifying a tell-tale inflection point in the spectrum. The rotation frequency is then proportional to the frequency of that inflection point. In this paper test this GPS method against available photometric records of the Sun. We apply GPS, autocorrelation functions, Lomb-Scargle periodograms, and wavelet analyses to the total solar irradiance (TSI) time series obtained from the Total Irradiance Monitor (TIM) on the Solar Radiation and Climate Experiment (SORCE) and the Variability of solar IRradiance and Gravity Oscillations (VIRGO) experiment on the SOlar and Heliospheric Observatory (SoHO) missions. We analyse the performance of all methods at various levels of solar activity. We show that the GPS method returns accurate values of solar rotation independently of the level of solar activity. In particular, it performs well during periods of high solar activity, when TSI variability displays an irregular pattern and other methods fail. Our results suggest that the GPS method can successfully determine the rotational periods of stars with both regular and non-regular light-curves.