# Holonomy of a triangle in an affine symmetric space

Let $$G/H$$ be an affine symmetric space with involution $$\sigma$$, and $$\mathfrak{g}=\mathfrak{m}\oplus \mathfrak{h}$$ the Cartan decomposition of its Lie algebra. We can identify $$G/H$$ and $$\exp(\mathfrak{m})$$. Given $$p,q\in \exp(\mathfrak{m})$$, I am wondering how to compute the holonomy of the curve formed by the geodesic segments, $$e\rightarrow p$$, $$p\rightarrow q$$, $$q\rightarrow e$$, $$e$$ being the identity. If I understand correctly, the holonomy should be given by a $$Ad_k$$ with $$k\in H$$. Can we compute $$k$$ in closed form from $$p$$ and $$q$$? I suspect it might be possible but I didn't manage.