A value of θ ∈(0, π / 3), for which |1+ cos^2 θ, sin^2 θ, 4 cos 6 θ; cos^2 θ, 1+ sin^2 θ, 4 cos 6 θ; cos^2 θ, sin^2 θ, 1+4 cos 6 θ| =0, is:

A value of $\displaystyle \theta \in(0, \pi / 3)$, for which $$\left|\begin{array}{ccc} 1+\cos ^2 \theta & \sin ^2 \theta & 4 \cos 6 \theta \\ \cos ^2 \theta & 1+\sin ^2 \theta & 4 \cos 6 \theta \\ \cos ^2 \theta & \sin ^2 \theta & 1+4 \cos 6 \theta \end{array}\right|=0, \text { is : } $$