According to Marius's law I=I0*cosθ *cosθ.
1. Under the condition of maximum transmitted light intensity, the polarization directions of the two polarizers should be the same. At this time, the transmitted light intensity should be 1/2 of the incident light intensity. As the name implies, when the transmitted light intensity is 1/3 of the maximum transmitted light intensity, that is, 1/6 = 1/2 * cos θ.
2. We still get θ = 35.3 from Marius's law1/3 =1/2 * cos θ * cos θ.