Prove that
`cos^(4)pi/8+cos^(4)(3pi)/(8)+cos^(4)(5pi)/8+cos^(4)(7pi)/8=3/2`

Explanation

To prove that

\[ \cos^4\left(\frac{\pi}{8}\right) + \cos^4\left(\frac{3\pi}{8}\right) + \cos^4\left(\frac{5\pi}{8}\right) + \cos^4\left(\frac{7\pi}{8}\right) = \frac{3}{2}, \]

we will simplify the left-hand side step by step.

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