For which angles we know the $\sin$ value algebraically (exact)? For example:


*

*$\sin(15^\circ) = \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4}$

*$\sin(18^\circ) = \frac{\sqrt{5}}{4} - \frac{1}{4}$

*$\sin(30^\circ) = \frac{1}{2}$

*$\sin(45^\circ) = \frac{1}{\sqrt{2}}$

*$\sin(67 \frac{1}{2}^\circ) = \sqrt{ \frac{\sqrt{2}}{4} + \frac{1}{2} }$

*$\sin(72^\circ) = \sqrt{ \frac{\sqrt{5}}{8} + \frac{5}{8} }$

*$\sin(75^\circ) = \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}$

*?


Is there is a list of known exact values of $\boldsymbol \sin$ somewhere?
Found a related post here.

Algebraically exact value of Sine for all integer angles is possible. Please visit https://archive.org/details/ExactTrigonometryTableForAllAnglesFinal for the list of exact values for Sine of integer angles in degrees.
