Given that cosec θ = −2, tan θ = 1/3√3 and −π < θ < π, find the exact

value of the angle θ in radians. Justify your answer.

so far i know that

sin θ = -1/2 θ = -π/6

tan θ = 1/√3 θ = π/6

from this i know that its in the third quadrant, does this mean the angle in radians im looking for is π/6?

any help would be great, thanks!