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Information on the rotation rate of the corona, and its variation over latitude and solar cycle, is valuable for making global connections between the corona and the Sun, for global estimates of reconnection rates, and as a basic parameter for solar wind modelling. Here, we use a time series of tomographical maps gained from coronagraph observations between 2007 - 2020 to directly measure the longitudinal drift of high-density streamers over time. The method reveals abrupt changes in rotation rates, revealing a complex relationship between the coronal rotation and the underlying photosphere. The majority of rates are between -1.0 to +0.5$^\circ$/day relative to the standard Carrington rate of 14.18$^\circ$/day, although rates are measured as low as -2.2$^\circ$/day and as high as 1.6$^\circ$/day. Equatorial rotation rates during the 2008 solar minimum are slightly faster than the Carrington rate, with an abrupt switch to slow rotation in 2009, then a return to faster rates in 2017. Abrupt changes and large variations in rates are seen at all latitudes. Comparison with a magnetic model suggests that periods of equatorial fast rotation are associated with times when a large proportion of the magnetic footpoints of equatorial streamers are near the equator, and we interpret the abrupt changes in terms of the latitudinal distribution of the streamer photospheric footpoints. The coronal rotation rate is a key parameter for solar wind models, and variations of up to a degree per day or more can lead to large systematic errors over forecasting periods of longer than a few days. The approach described in this paper gives corrected values that can form a part of future forecasting efforts.