Rational with finite decimals values for sine, cosine, and tangent What are the possible combinations of sine, cosine, and tangent values such that all three are simultaneously rational with finite decimals?

I am aware of the below two cases.


$\sin(x) = 0, \cos(x) = 1, \tan(x) = 0$ is a trivial case for angle measure zero
$\sin(x) = 0.6, \cos(x) = 0.8, \tan(x) = 0.75$ is another case, for an angle of $37$ degrees (approximately)


Are there any other combinations that satisfy the condition? If not, is it possible to prove that these are the only possible combinations?

Edit: Sorry, I missed one detail when posting the question. I am looking for sin, cos and tan values being rational numbers with finite decimals. For example, (7, 24, 25) is a Pythagorean triple that does not satisfy the condition because tan value would be 0.291666....
Any Pythagorean triple will give you rational $\sin, \cos, \tan$ values, and any triple of rational trig values will give you a Pythagorean triple.

The Pythagorean triples have been completely classified. Take two natural numbers $u&gt;v$. Then
$$
(u^2-v^2)^2 + (2uv)^2=(u^2+v^2)^2
$$
and any Pythagorean triple is either of this form or a multiple of such a triple. So the possible rational $\sin$ and $\cos$ pairs are all possible values of
$$
\frac{u^2-v^2}{u^2+v^2}\text{ and }\frac{2uv}{u^2+v^2}
$$
Have you tried using base $6$? I have heard that doing so can result in more accurate results when using $\pi$. It may also work better in this case, as the desired result are finite decimals.