  Assuming a static and spherically symmetric spacetime, we propose a novel
concept of the total deflection angle of a light ray. The concept is defined by
the difference between the sum of internal angles of two triangles; one of the
triangles lies on curved spacetime distorted by a gravitating body and the
other on its background. The triangle required to define the total deflection
angle can be realized by setting three laser-beam baselines as in planned space
missions such as LATOR, ASTROD-GW, and LISA. Accordingly, the new total
deflection angle is, in principle, measurable by gauging the internal angles of
the triangles. The new definition of the total deflection angle can provide a
geometrically and intuitively clear interpretation. Two formulas are proposed
to calculate the total deflection angle on the basis of the Gauss--Bonnet
theorem. It is shown that in the case of the Schwarzschild spacetime, the
expression for the total deflection angle $\alpha_{\rm Sch}$ reduces to
Epstein--Shapiro's formula when the source of a light ray and the observer are
located in an asymptotically flat region. Additionally, in the case of the
Schwarzschild--de Sitter spacetime, the expression for the total deflection
angle $\alpha_{\rm SdS}$ comprises the Schwarzschild-like parts and coupling
terms of the central mass $m$ and the cosmological constant $\Lambda$ in the
form of ${\cal O}(\Lambda m)$ instead of ${\cal O}(\Lambda/m)$. Furthermore,
$\alpha_{\rm SdS}$ does not include the terms characterized only by the
cosmological constant $\Lambda$.
