How to calculate asymptotic of Supertransparent potential of the Dirac equation?

Question

The Supertransparent potential of the Dirac equation

$v(x)= \frac{4\lambda_{1}(\sin2\theta-2\lambda_{1}\gamma \cos2\theta)}{\sin^{2}2\theta-4\lambda_{1}^{2}\gamma^{2}},\quad (1)$

where

$\theta=\lambda_{1}(x+x_{1}(\lambda_{1})),\; \gamma = x+x_{2},\; x_{2} = x_{1}+\lambda_{1}\partial_{\lambda_{1}}x_{1}(\lambda_{1})$.

This potential has obviously two first-order poles determined by

$\sin^{2}2\theta-4\lambda_{1}^{2}\gamma^{2}=0,$

whose exact location can be fine-tuned by the choice of the parameters $\lambda_{1},\;x_{1}$ and $x_{2}$ . For $x \rightarrow \pm \infty$, one obtains the asymptotic estimate

$v(x) = \frac{2}{\lambda_{1}x}\cos2\theta\left[1+O(\frac{1}{x})\right] \quad (2)$

How to get (2) from (1)?