= Solution
A <plane> through the origin has equation $lx+my+nz=0$ for some nonzero normal $(l,m,n)$. Dividing that normal by its <Euclidean norm> makes $l^2+m^2+n^2=1$ without changing the <plane>. Substitute the <spherical coordinates> from (a) and cancel the nonzero radius:
$$
\boxed{l\sin\theta\cos\phi+m\sin\theta\sin\phi+n\cos\theta=0,\qquad
l^2+m^2+n^2=1}.
$$
Its intersection with the <sphere> is the desired <great circle>; changing the sign of all three coefficients describes the same <circle>.
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