We always use inverse trig functions (arc trig) to solve for angles in trig equation.
If tanx = 2.3 , then x = tan-1(2.3), so use a calculator to get your 1st solution (will be 0 < x < π/2). Then, to find a second solution between 0 and 2π, add π to the answer you just got.
For tan equations, you always add π to the 1st solution. For sine equations, we do π - 1st solution. For cosine equations, we do 2π - 1st solution. Lastly, if sinx or tanx = a negative number, arctan or arcsin will give you a - angle. Add 2π to this number to get a solution in the domain [0 , 2π).