So we can express trigonometric quantities in terms of Spherical harmonics, for example $\cos(\theta)\propto Y^{0}_{1}(\theta,\phi)$. Is there a closed expression for $\sin(\theta)$? If not, is there at least some kind of convoluted, numerically accessible expression?
Best,
v.
PS: It seems to be an infinite sum of $Y_{l}^0$ with even $l$, have a look at my numerical estimate:
