Sin 3°

What is the sine of three degrees? This is the smallest angle with an integer number of degrees whose trig functions are algebraic. This means that they can be written as integers combined with the operations of addition, subtraction, multiplication, division, and radicals. Trig functions of angles which are not multiples of three are transcendental. The best we can do to represent them is a decimal approximation.

Your job is to find an exact, algebraic value for Sin 3°. Simplify your answer as much as you can, and be sure to show all the steps in your solution!