Should people who are taking supplemental EPA/DHA also be taking a vitamin E supplement?

There are some human studies showing a decrease in blood levels of vitamin E in those who are taking supplemental EPA/DHA without any concomitant increased intake of vitamin E. Enriching human cells and tissues with omega-3 fatty acid often requires adequate membrane levels of vitamin E (alpha-tocopherol) as an antioxidant to protect cells from oxidative stress. Thus, many omega-3 supplements contain a few milligrams (or international units) of vitamin E.