How to find values for x where tan(x)=ComplexInfinity

Questions
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1

I’m trying to calculate values for x where tan(x)=ComplexInfinity. For this I just expected to input tan(x)=ComplexInfinity however, the system doesn’t seem to understand this input.

For example, if enter sin(x)=1 it returns a solution: 1/2(4?n+?). I’m trying to get a similar output for the formula above.

tan(x) first reaches CompexInfinity at ?/2, then has a period of ?, so I expect a result should be possible.

Does anyone know if I am inputting this incorrectly, or is this not possible in the system?

Regards,
Nick

2

In[1]:= Reduce[Tan^-1 == 0, x, Reals]

Out[1]= C[1] \[Element] 
  Integers && (x == -(\[Pi]/2) + 2 \[Pi] C[1] || 
   x == \[Pi]/2 + 2 \[Pi] C[1])