Answer
Please see the work below.
Work Step by Step
We know that the transmitted intensities will be the same, if the incident light is polarized in a direction which makes an angle $\frac{1}{2}\theta$ with the vertical. Thus, in this case, both experiments give a transmitted intensity equal to $I_{\circ}(cos\frac{1}{2}\theta)^2(cos\theta)^2$, where $I_{\circ}$ shows the incident intensity.
