Hint:

tan θ = -2.662 and cos θ > 0

so

θ in the 4th quadrant

tan T = -2.662

cos T > 0 so T lies in quadrant IV

T = arctan(-2.662) =-1.21145

The angle in the fourth quadrant is 2pi-1.21145 = 5.0717 radian (290.59 degrees)

290.589° = 5.072 radians

arctan ( - 2.662 ) + 2π

cosθ > 0 ⇒ θ is in Quadrant I or IV

tanθ < 0 ⇒ θ is in Quadrant II or IV

∴ θ is in Quadrant IV

θ = arctan(-2.662) ≅ 290.6°