1.
The number of θ(0,4π)\theta \in (0, 4\pi) for which the system of linear equations
3sin3θxy+z=23\sin 3\theta \, x - y + z = 2

3cos2θx+4y+3z=33\cos 2\theta \, x + 4y + 3z = 3

6x7y+7z=96x - 7y + 7z = 9

has no solution is: