= Solution
Insert the diagonal covariance from <3/a> into the two-point function and apply the <spherical harmonic addition theorem>:
$$
C(\alpha)=\sum_l C_l\sum_{m=-l}^l\mathcal Y_{lm}(\hat n)\mathcal Y_{lm}^*(\hat m)
=\boxed{\frac{1}{4\pi}\sum_{l=0}^\infty(2l+1)C_lP_l(\cos\alpha)}.
$$
The <Legendre polynomials> encode the angular separation. Since $P_l(1)=1$, the zero-separation value $C(0)=\langle\Theta^2\rangle$ is the total <variance>. For measured <Cosmic microwave background anisotropy>, remove the monopole and usually the kinematic dipole, so the corresponding sum starts at $l=2$; an instrument's angular response supplies an additional window function.
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