Well arccos(–*θ*) = π – arccos(*θ*), so we have that
arccos(cos*c*) = *c* =  arccos(-1/2) = π – arccos(1/2) = π – π/3
The reference angle=pi/3.

Cosine is negative in Q2 and Q3.

This is a triangle, so C must be in Q2.

In Q2, θ=pi-θref

C=pi-pi/3=2pi/3