The downside to this approach is that the last \right) does not realize it should be the same size as the first \left(, but I am tempted to call this good enough.
s = L"""
$\Delta\epsilon_{peqk} = \frac{\sqrt{2}}{3} \cdot \left[ \left( \Delta\epsilon_{p11k} - \Delta\epsilon_{p22k} \right)^{2} + \left( \Delta\epsilon_{p22k} - \Delta\epsilon_{p33k} \right)^{2} + \left( \Delta\epsilon_{p33k} - \Delta\epsilon_{p11k} \right)^{2} \right.$
$\vdots$
$+ \left. 1.5 \cdot \left( \Delta\epsilon_{p12k}^{2} + \Delta\epsilon_{p23k}^{2} + \Delta\epsilon_{p31k}^{2} \right) \right]^{0.5}$
"""
render(s)
