Sums and products of cosines of pi/8, 3pi/8, 5pi/8, 7pi/8

This type of question, asked 2 times: 10 May 2023 S1, 25 Apr 2025 S2. All 2 questions below, oldest first.

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Question 1
10 May 2023 S1
126 $\left(1+\cos\frac{\pi}{8}\right)\!\left(1+\cos\frac{3\pi}{8}\right)\!\left(1+\cos\frac{5\pi}{8}\right)\!\left(1+\cos\frac{7\pi}{8}\right)$
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Question 2
25 Apr 2025 S2
148 $\cos^{4}\frac{\pi}{8}+\cos^{4}\frac{3\pi}{8}+\cos^{4}\frac{5\pi}{8}+\cos^{4}\frac{7\pi}{8}=$
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