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

Explanation

To prove that

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

we will follow these steps:

...