If sin θ_1</s

Given that sin θ₁ + sin θ₂ + sin θ₃ = 3

We know that in general the maximum value of sin θ = 1 when θ = π/2

As sin θ₁ + sin θ₂ + sin θ₃ = 3

⇒ θ₁= θ₂ = θ₃ = π/2.

The above case is the only possible condition for the given condition to satisfy.

∴ cos θ₁ + cos θ₂ + cos θ₃

⇒ cos π/2 + cos π/2 + cos π/2

⇒ 0+0+0

⇒ 0.