Given cosecθ= -2, tanθ= 1/3√3 and -π < θ < π.

I must find the exact value of θ in radians, justifying my answer.

It shouldn't be too difficult;

An answer is

cosec theta = -2 implies sin theta = -(1/2); value of tan theta cannot be (1)/(3)√(3) but if it is taken as 1/√(3); then required theta = -(5*pi/6).

Or is this incorrect?