The value of $\cos^4\frac{\pi}{8} + \cos^4\frac{3\pi}{8}+\cos^4\frac{5\pi}{8}+\cos^4\frac{7\pi}{8}$ Problem : 
The value of $\cos^4\frac{\pi}{8} + \cos^4\frac{3\pi}{8}+\cos^4\frac{5\pi}{8}+\cos^4\frac{7\pi}{8}$
If this could have been like this $\cos\frac{\pi}{8} + \cos\frac{3\pi}{8}+\cos\frac{5\pi}{8}+\cos\frac{7\pi}{8}$ then we can take the terms like 
$(\cos\frac{3\pi}{8}+\cos\frac{5\pi}{8} ) + (\cos\frac{\pi}{8} +\cos\frac{7\pi}{8})$
and solve further , but in this case due to power of 4 I am unable to proceed please suggest... thanks..

HINT 
From $\cos(2x) = 2 \cos^2(x) - 1$, replace each term already squared by something which looks that the cosine of the double angle. Since your base angle is $\pi/8$, the double angle is $\pi/4$ and you know the value of the cosine of this angle.
I am sure you can take from here.
