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IMO Shortlist 1962 problem 4

1962 IMO shortlist
Solve the equation \cos^2{x}+\cos^2{2x}+\cos^2{3x}=1

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Task list
#TitleTagsSol.QualityDifficulty
1558IMO Shortlist 1981 problem 1
1981 IMO shortlist tb
1
1592IMO Shortlist 1982 problem 16
1982 IMO shortlist tb
1
1642IMO Shortlist 1985 problem 1
1985 IMO shortlist tb
2
1711IMO Shortlist 1988 problem 4
1988 IMO komb shortlist
1
1808IMO Shortlist 1991 problem 10
1991 IMO shortlist
1
1960IMO Shortlist 1997 problem 4
1997 IMO shortlist
2