How do you find an exact value for sin of 40 degrees without using a calculator

Sin 40° + sin 130° + sin 220° + sin 310° = ...
sin 130° = sin 50°;
sin 220° = - sin 40°;
sin 310° = - sin 50°
... = sin 40° + sin 50° - sin 40° - sin 50° = 0
0.