You don't unscrew the mast with the antenna in the car, you remove the antenna first. It pulls through the rubber grommet once you remove the antenna bracket bolt, electrical connection and drain tube. Once you remove the antenna from the car, you'll see there are about 5 or 6 clips that hold the two halves of the antenna housing together. There are also 3 or 4 rivets that must be drilled out. Once you have it apart, you can remove the mast. Usually the nylon cord that moves the mast up and down breaks.
http://www.antennamastsrus.com/GM/Buick/Riviera/Riviera%201995-1999.htm
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98 Riviera SC3800 All stock except gutted air box.
1970 Buick GS455 Stage1, TSP built 470BBB, 602HP/589TQ
Best MPH, 116.06 MPH, Best ET, 11.54
https://www.youtube.com/watch?v=UHCda-t_Jls
https://www.youtube.com/watch?v=sfT2tEO4XcU