Let us say that u get solutions as -
tanx = something1
cosy = something2
sinz = something3
Since they explicitly say that there are solutions in 0-2pi, we know that there exists real solutions for the above 3 equations. Now, there will be atleast 2 solutions for tanx, cosy and sinz in 0-2pi. So 2x2x2 combinations means n should be atleast 8.