let f(θ)=sin2⁡θcos2⁡θ1+4sin⁡4θsin2⁡θ1+cos2⁡θ4sin⁡4θ1+sin2⁡θcos2⁡θ4sin⁡4θ then f is

f(θ)=−101−1101+sin2⁡θcos2⁡θ4sin⁡2θ                                              (R1→R1-R3   R2 →R2-R3)=001−1101+sin2⁡θcos2⁡θ4sin⁡4θ+4sin⁡4θ   (C1 →C1 + C3)=−cos2⁡θ+1+sin2⁡θ+4sin⁡4θ⇒-2(1+2sin 4 θ)which is periodic function with period 2π4=π2.