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Consider the Poincare half-plane model of hyperbolic geometry. Consider the polygon, bounded by the following 4 curves: $x=-2a, (x+2a)^2+y^2=36a^2,(x+a)^2+y^2=a^2,(x-2a)^2+y^2=4a^2$. By what angle will a vector rotate after parallel transport along this polygon?

I don't know how to solve this problem. I suppose the fact that all these curves are geodesic should make this problem easy, yet I do not know how to use this fact.

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    $\begingroup$ Hint: compute the angle deficit of your polygon. $\endgroup$
    – Moishe Kohan
    Commented May 19 at 15:15

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