we have to:
cos θ = 1/4
Clearing the angle we have:
θ = ACOS (1/4) = 1.318116072
As sin θ <0 then the angle measured from the x axis and counterclockwise is
2 * pi-1.318116072 = 4.965069236
For this angle, the tangent is
tan θ = sin θ / cos θ = -0.968245837 / 0.25 = -3.872983346
answer
tan θ = -3.872983346
