Industrialization and modern methods of insect control have improved the standard of living around the globe while at the same time they have introduced some 100,000 dangerous chemical pollutants, having gone virtually unregulated since they were developed more than 50 years ago.
while at the same time they have introduced some 100,000 dangerous chemical pollutants, having
while at the same time introducing some 100,000 dangerous chemical pollutants that have
while they have introduced some 100,000 dangerous chemical pollutants at the same time, which have
but introducing some 100,000 dangerous chemical pollutants at the same time that have
but at the same time introducing some 100,000 dangerous chemical pollutants, having
so you just have to memorize which ones can do which.
in this case, you've just learned that "while" can be followed by an -ing participle. (it can also be followed by an adjective or adjective phrase.)
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