1.
Let θ(0,π2)\theta \in (0, \frac{\pi}{2}). If the system of linear equations
(1+cos2θ)x+sin2θy+4sin3θz=0,(1 + \cos^2 \theta) x + \sin^2 \theta \, y + 4 \sin 3\theta \, z = 0,

cos2θx+(1+sin2θ)y+4sin3θz=0,\cos^2 \theta \, x + (1 + \sin^2 \theta) y + 4 \sin 3\theta \, z = 0,

cos2θx+sin2θy+(1+4sin3θ)z=0\cos^2 \theta \, x + \sin^2 \theta \, y + (1 + 4 \sin 3\theta) z = 0

has a non-trivial solution, then the value of θ\theta is: