Complexity! (3)

Algebra Level 3

If $$z$$ is a complex number of unit modulus whose argument is $$\theta$$, find $$\arg \left( \dfrac{1+z}{1+\bar{z}} \right)$$.

Notations:

• $$\bar{z}$$ denotes the conjugate of $$z$$.
• $$\arg (\cdot)$$ denotes the argument of a complex number.