= Solution
At the chosen event use the <orthonormal frame in spacetime> from the hint. The electromagnetic energy density is
$$
\rho=T_{00}=\frac12(|\mathbf E|^2+|\mathbf B|^2),
$$
and the energy flux is the <Poynting vector> $\mathbf S=\mathbf E\times\mathbf B$. Depending on the index convention, the required contraction is $\rho-wS_1$ or $\rho+wS_1$. In either case,
$$
T_{ab}V^aW^b\geq\rho-|\mathbf S|
\geq\frac12(|\mathbf E|^2+|\mathbf B|^2)-|\mathbf E||\mathbf B|
=\frac12(|\mathbf E|-|\mathbf B|)^2\geq0.
$$
Rescaling $V$ and rotating the spatial frame covers arbitrary future timelike $V$ and future causal $W$. Thus the Maxwell field satisfies the <dominant energy condition>.
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