Let $p_0$ be a pole of a unit sphere $S^2$ and $q$, $r$ be two points on the corresponding equator in such a way that the meridians $p_0q$ and $p_0r$ make an angle $ heta$ at $p_0$. Consider a unit vector $v$ tangent to the meridian $p_0q$ at $p_0$, and take the parallel transport of $v$ along the closed curve made up by the meridian $p_0q$, the parallel $qr$, and the meridian $rp_0$ (Fig. 4-21).
a. Determine the angle of the final position of $v$ with $v$.
b. Do the same thing when the points $r$, $q$ instead of being on the equator are taken on a parallel of colatitude $phi$ (cf. Example 1).