I am looking for a form of $$\cos^2\theta\cos\phi\sin\phi=\sum_{lm}c_{lm}Y_l^{m}(\theta,\phi),$$ where $Y_{lm}$ is the spherical harmonics. The idea I believe would be to find $$c_{lm}=\int_0^{2\pi}\int_0^\pi \mathrm{d\theta}\sin\theta\mathrm{d\phi}Y_{lm}^*(\theta,\phi)\cos^2\theta\cos\phi\sin\phi.$$ But I am unable to solve the above integral. Any idea on how to obtain full expression in terms of spherical harmonics?
2026-04-07 21:20:15.1775596815
Express $\cos^2\theta\cos\phi\sin\phi$ in Spherical Harmonics
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