Two polaroids are placed in the path of unpolarized beam of intensity I0 such that no light is emitted from the second polaroid. If a third polaroid whose polarization axis makes an angle θ with the polarization axis of first polaroid, is placed between these polaroids then the intensity of light emerging from the last polaroid will be

(1) $\left(\frac{{I}_{0}}{8}\right){\mathrm{sin}}^{2}2\theta$

(2) $\left(\frac{{I}_{0}}{4}\right){\mathrm{sin}}^{2}2\theta$

(3) $\left(\frac{{I}_{0}}{2}\right){\mathrm{cos}}^{4}\theta$

(4) ${I}_{0}{\mathrm{cos}}^{4}\theta$