1.
A value of θ∈(0,π3)\theta\in\left(0,\frac{\pi}{3}\right), for which
∣1+cos⁡2θsin⁡2θ4cos⁡6θcos⁡2θ1+sin⁡2θ4cos⁡6θcos⁡2θsin⁡2θ1+4cos⁡6θ∣=0\begin{vmatrix} 1+\cos^{2}\theta & \sin^{2}\theta & 4\cos6\theta \\ \cos^{2}\theta & 1+\sin^{2}\theta & 4\cos6\theta \\ \cos^{2}\theta & \sin^{2}\theta & 1+4\cos6\theta \end{vmatrix}=0

is: