Verified answer

(tan θ + 1)(cos θ + 1) = 0

tan θ cos θ + tan θ + cos θ + 1 = 0

sin θ + tan θ + cos θ + 1 = 0

sin θ cos θ + sin θ + cos^2 θ + cos θ = 0

cos θ (sin θ + cos θ) + (sin θ + cos θ) = 0

(sin θ + cos θ) (cos θ + 1) = 0

cos θ + 1 = 0 ==> cos θ = -1 ==> θ = π rad = 180° (Answer)

sin θ + cos θ = 0 ==> sin θ = -cos θ ==> θ = 3π/4 or 7π/4 rad = 135° or 315° (Answer)

These last two solutions are in the 2nd & 4th quadrants.

tanΘ = -1 or cosΘ = -1

Θ = 135º, 315º, or 180º

This makes use of basics that should be memorized-

ref angle 45º

Q2, Q4

quadrantal angles