About Sign
A sign is 30 degrees, one twelfth of a circle, or π/6 (0.5236) radians. It comes from the 12 signs of the zodiac, each covering 30° of the ecliptic, and the word is from the Latin signum, a mark.
About US WW2 Milliradians
The US wartime mil was an artillery unit, a rounded milliradian, and a right angle came to exactly 1,000 of them (4,000 to a circle). A true milliradian is smaller: 6,283 fit in a circle.
In World War II American artillery crews set elevation and direction in mils, reading the angle between the target and the gun from an aiming circle.
There are 4,000 US WW2 milliradians in a full circle.