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IMO Shortlist 1967 problem 3

1967 shortlist
Without using tables, find the exact value of the product:
P = \prod^7_{k=1} \cos \left(\frac{k \pi}{15} \right).

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1967 shortlist
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1967 shortlist
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1967 shortlist
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1967 shortlist
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1967 shortlist
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1967 shortlist
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