Partial Derivatives & the Gradient · Superchallenge problem

The sphere $x^2 + y^2 + z^2 = 9$ and the paraboloid $z = x^2 + y^2 - 3$ meet in a circle (and one isolated point). At each point of that circle the two surfaces cross at the same angle $\theta$, the acute angle between their normal lines. Find $\cos\theta$.