Sign error when deriving Weyl spinor transformation laws (3.37) in Peskin Schroesder

I am having some trouble deriving the transormation laws for the weyl spinors, equation (3.37) in the Peskin Schroesder book on quantum field theory.

Beginning with the relation $psito(1-frac{i}{2}omega_{munu}S^{munu})psi$ from (3.30) and the form of the transformation matrices in equations (3.26) and (3.27), I get

$1-frac{i}{2}omega_{munu}S^{munu} = 1-frac{i}{2}omega_{0nu}S^{0nu} + frac{i}{2}omega_{inu}S^{inu} = 1 – frac{i}{2}omega_{00}S^{00} + frac{i}{2}omega_{0i}S^{0i} + frac{i}{2}omega_{i0}S^{i0} – frac{i}{2}omega_{ij}S^{ij}$

$ = 1 – 0 + iomega_{0i}S^{0i} – frac{i}{2}omega_{ij}S^{ij} = 1+iomega_{0i}frac{-i}{2}begin{pmatrix}sigma^i & 0 0 & -sigma^iend{pmatrix} – frac{i}{2}omega_{ij}frac{1}{2}epsilon^{ijk}begin{pmatrix}sigma^k & 0 0 & sigma^kend{pmatrix} $

The discussion at the end of section 3.1, leading to equations (3.20) and (3.21) then suggest the identification $omega_{0i} = beta_i$ and $omega_{ij} = epsilon_{ijk}theta^k$. Plugging this in gives

$1 + frac{1}{2}beta_ibegin{pmatrix}sigma^i & 0 0 & -sigma^iend{pmatrix} + frac{1}{4}epsilon_{ijl}theta^lepsilon^{ijk}begin{pmatrix}sigma^k & 0 0 & sigma^kend{pmatrix}$

Using the identitiy $epsilon_{ijl}epsilon^{ijk} = 2delta_l^k$ gives

$1 + frac{1}{2}beta_ibegin{pmatrix}sigma^i & 0 0 & -sigma^iend{pmatrix} + frac{1}{2}theta^kbegin{pmatrix}sigma^k & 0 0 & sigma^kend{pmatrix}$

$ = begin{pmatrix}1 + frac{1}{2}beta_isigma^i – frac{1}{2}theta^ksigma^k & 0 0 & 1 – frac{1}{2}beta_isigma^i – frac{1}{2}theta^ksigma^k end{pmatrix}$

$ = begin{pmatrix}1 – frac{1}{2}vec{theta}cdotvec{sigma} + frac{1}{2}vec{beta}cdotvec{sigma} & 0 0 & 1 – frac{1}{2}vec{theta}cdotvec{sigma} – frac{1}{2}vec{beta}cdotvec{sigma} end{pmatrix}$

Making the identification $psi = begin{pmatrix}psi_L psi_Rend{pmatrix}$, this then gives

$psi_Lto(1 – frac{1}{2}vec{theta}cdotvec{sigma} + frac{1}{2}vec{beta}cdotvec{sigma})psi_L$

$psi_Rto(1 – frac{1}{2}vec{theta}cdotvec{sigma} – frac{1}{2}vec{beta}cdotvec{sigma})psi_R$

for the Weyl transformations, which is the oposite order to how it appears in the book. Given that it is only a small difference, I initially thought it might just be a typo in the book, although I encountered similar sign errors later that lead me to think this calculation is wrong, although I can’t seem to find where.