U(n)/L(n) = 3

For every integer n > 2 let L(n) denote the sum of the integers from 1 through
[n/2] which are relatively prime to n, and let U(n) denote the sum of the integers
from [n/2] + 1 through n which are relatively prime to n. Prove that if n is
divisible by 4, then U(n)/L(n) = 3. ([ . ] is the greatest integer function.)