Let $M$ = $S^2$ = ${\{(x, y, z)\in\mathbb R}$; $x^2+y^2+z^2 = 1\}$
$\gamma = \gamma_1 \cup \gamma_2 \cup \gamma_3$ where $\gamma_j$, $j = 1, 2, 3$ is given below:
$\gamma_1 = \{(cost, sint, 0)\ |\ 0\le t\le \pi/2\}$
$\gamma_2 = \{(0, cost, sint)\ |\ 0\le t\le \pi/2\}$
$\gamma_3 = \{(sint, 0, cost)\ |\ 0\le t\le \pi/2\}$
with the increasing direction of $t$. Parallel transport the vector $V_0 = (0, 0, −1)$ at the starting point $p = \gamma_1(0)$, along $\gamma$, and return to $p$. Compute its holonomy angle.
This is what I have done so far, can someone please confirm if this is correct? http://imgur.com/a/CSgbn