1.
The number of θ(0,4π)\theta \in (0, 4\pi) for which the system of linear equations

3(sin3θ)x+y+z=23(\sin 3\theta)x + y + z = 2
3(cos2θ)x+4y+3z=33(\cos 2\theta)x + 4y + 3z = 3
6x+7y+7z=96x + 7y + 7z = 9

has no solution, is