The sum of the absolute squares of the spherical harmonics Y_l^m(θ, ϕ) over all values of m is sum_(m = - l)^l ( left bracketing bar Y_l^m(θ, ϕ) right bracketing bar )^2 = (2l + 1)/(4π). The double sum over m and l is given by sum_(l = 0)^∞ sum_(m = - l)^l Y_l^m(θ_1, ϕ_1)Y^__l^m(θ_2, ϕ_2) | = | 1/(sin θ_1) δ(θ_1 - θ_2) δ(ϕ_1 - ϕ_2) | = | δ(cos θ_1 - cos θ_2) δ(ϕ_1 - ϕ_2), where δ(x) is the delta function.