In the text "Functions of One Complex Variable" by Robert E. Greene and Steven G. Krantz, the authors give a tedious definition of $\eta_{R}$. What are alternate definitions ?
Background
$\text{Definition (1.1)}$
The author defines $\eta_{R}$ our Keyhole Contour such that $$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \eta_{R}^{1}(t) = t + i/\sqrt{2R}, \, \, \, \, 1/\sqrt{2R} \leq t \leq R,$$
$$\eta_{R}^{2}(t)= Re^{it}, \, \, \, \, \theta_{0} \leq t \leq 2 \pi - \theta_{0},$$
where $\theta_{0} = \theta_{0}(R) = \sin^{-1}(1/(R \sqrt{2R}))$
$$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \eta_{R}^{3}(t) = R -t -i/\sqrt{2R}, \, \, \, \, 0 \leq t \leq R-1/\sqrt{2R},$$
$$\eta_{R}^{4}(t) = e^{it}/\sqrt{R}, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \pi/4 \leq t \leq 7 \pi /4.$$
$\text{Remark}$
For those who don't have the text a picture has been provided for convenience
$\text{Figure (1.1)}$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, $ 
The picture is worth a thousand words. $\eta_R$ is a parametrization of the contour that goes at height $1/\sqrt{2R}$ above the positive real axis from the inner circle to the outer circle, then counterclockwise around the outer circle to $1/\sqrt{2R}$ below the positive real axis, then horizontally left to the inner circle, and finally clockwise around the inner circle to the starting point.