Answer
$\theta=45^{\circ}$
Work Step by Step
When the polarizers are aligned, and $I_1$ is the intensity after the first Polaroid, that is also the intensity after the second (by equation 24-5 with zero angle).
Now we want a reduction to half intensity.
Use equation 24–5 to relate the final intensity to $I_1$.
$$0.5 I_1=I_1cos^2\theta$$
$$0.5 =cos^2\theta$$
$$\theta=45^{\circ}$$
