Compute the geodesic curvature of any sphere on a sphere.

Question

Compute the geodesic curvature of any sphere on a sphere.

---

Again there exists its answer, but not understandable for me. Please explain it explicitly. Thank you so much.

(If required, i can post the answer)

The answer is the following post;

Answer 1

Some thing are assumed in posted answer:

1. For any curve $\alpha$ passing throw $p$ and tangent to curve be tangent to latitude, direction of normal of curve is it's perpendicular to $z$-axis.
2. With Eq. 7.10 which you can see but I can't we have geodesic curvature of such $\alpha$ is$\kappa_g=\pm \frac 1 r \sin\theta$.
3. The angle which showed below means $\theta$.

Now proof is so easy to see in the above we have $r=R \cos\theta$ so we have $\kappa_g=\pm \frac 1 R \tan\theta$. So $\kappa_g$ is zero iff $\theta=0$, which means $p$ lies on great circle.
If need more detail just mention.