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

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