Where are the singularities of f(z) = Log(2+tan(z)) located?

[Gallani]

I need to find the locations of the singularity of f(z) = Log(2+tan(z)).

So far I have looked at the function in its alternate form

Log(2+tan(z)) = ln(abs(2+tan(z))) + i*Arg(2+tan(z))

If I remember correctly the first part is simple and cannot equal zero.

Now I think the second part is defined on the cut 0 to 2∏ which eliminates the negative imaginary axis.

 

[jedishrfu]

first determine what x makes log(x) a singularity then determine how x can be assigned that value by2+tan(z)