Find tan θ if cos θ = one divided by four and sin θ < 0

In this case we have:
 cos θ = 1/4
 Whose possible solutions are:
 θ = 2 * pi * n - Acos (1/4)
 θ = 2 * pi * n + Acos (1/4)
 Where,
 n belongs to the natural numbers.
 As sin θ <0 then the solution is:
 θ = 2 * pi * n - Acos (1/4)
 For n = 1 we get:
 θ = 4.965069236 radians
 Thus:
 tan θ = tan (4.965069236) = - 3.872983346
 
 tan θ = -3.872983346

Magic man is here, but unfortunately he is broke won’t you him out