State domain, range, period, vertical asymptotes, zeros, symmetry and y-intercept of 3y=-2\tan \left ( 3x+180^{\circ} \right )+3 .

State domain, range, period, vertical asymptotes, zeros, symmetry and y-intercept of .

I usually have trouble identifying domain, vertical asymptotes, zeros, and symmetry for tangent functions.

My attempt:

Domain

Same as asymptotes: 

Range



Period



Vertical asymptotes

Using the quotient identity:  and setting the denominator to zero:















Add  to find more asymptotes:

Asymptotes 

Zeros



















Add  to find more zeros:

Zeros = 

Symmetry

?

Y-intercept: (0, 3)











Please verify and show all work.

Some explanation for finding domain, vertical asymptotes, zeros, and symmetry for tangent functions (using degrees not radians) would be great.