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Question: Little puzzle by the way

Question:Little puzzle by the way

Alfred_F 325 Maple 2024
summation
June 25 2025
1

The attached problem is from a 1988 MO. It can be solved using complete induction, paper, and pencil, and with some effort, yields a simple answer. It's quite challenging to do by hand, but with "derive", it only takes three lines and a fraction of a second. Mow test.mw

restart

"puzzle(n):=(∑)(cos(k*Pi/(2*n+1))^())^(4);"

Download test.mw

I can't do it with Maple because I'm doing something wrong again. Therefore, I'm asking for help.
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