Find the value of
`cos^2. pi/16+cos^2. (3pi)/16+cos^2. (5pi)/16+cos^2. (7pi)/16`.

Explanation

To find the value of \( \cos^2 \frac{\pi}{16} + \cos^2 \frac{3\pi}{16} + \cos^2 \frac{5\pi}{16} + \cos^2 \frac{7\pi}{16} \), we can follow these steps:

1. **Rewrite the terms**: We can express \( \cos^2 \frac{5\pi}{16} \) and \( \cos^2 \frac{7\pi}{16} \) using the identity \( \cos^2 \left( \frac{\pi}{2} - x \right) = \sin^2 x \).

\[ \cos^2 \frac{5\pi}{16} = \cos^2 \left( \frac{\pi}{2} - \frac{3\pi}{16} \right) = \sin^2 \frac{3\pi}{16} \]
\[
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