sphericalharmonicy – Confirming orthogonality of spherical harmonics symbolically

One can confirm the orthogonality of the SphericalHarmonicYs for specific values of their parameters (l, m, ll, mm) as I showed in my solution here, but I have been unable to verify it for the general case, as in:

Assuming({l, ll, m, mm} ∈ Integers && 
   -l <= m <= l && -ll <= mm <= ll , 
    SphericalHarmonicY(l, m, ϑ, φ)) 
    SphericalHarmonicY(ll, mm, ϑ, φ) 
  {ϑ, 0, π}, {φ, 0, 2 π}))

Are there any tricks, or assumptions, or other techniques that enable Mathematica to symbolically evaluate that integral (leading to a product of KroneckerDelta functions)? I even tried FunctionExpand to express each SphericalHarmonicY using exponentials and other simpler functions, but the integral was still not evaluated.