A value of θ∈(0,π/3) for which |1+cos2θsin2θ4cos6θcos2θ1+sin2θ4cos6θcos2θsin2θ1+4cos6θ|=0, is

Correct option is C. π9
R1→R1−R2|1−1;0cos2θ1+sin2θ4cos6θcos2θsin2θ1+4cos6θ|=0
R2→R2−R3|1−1;001−1;cos2θsin2θ1+4cos6θ|=0
→(1+4cos6θ)+sin2θ+1(cos2θ)=0
1+2cos6θ=0
→cos6θ=−1/2;
6θ=2π3
→θ=π9.