Question

How many values of θ will satisfy tan-1 0 = θ when 0º<θ<90º?

Answer 1

We want to satisfy
tan⁻¹ 0 = θ when 0° < θ < 90°.

The restriction on θ places the angle in the 1st quadrant.
When tan θ = 0, θ = 0°, 180°, 360°, ...
If θ >= 0, then a solution exists in the 1st quadrant.
Because of the requirement θ>0, no answer satisfies the given equation.

Answer: None