Confusion about variables in polar coordinates

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Homework Statement

x

Relevant Equations

x

My confusion refers to this question above.

If I were to ask you, what is the equation of the radial line, what would you say? I know that the general equation the radial line with cartesian gradient of m has an equation of θ = arctan(m). Clearly here the angle between the radial line and initial line is θ, therefore the equation is θ = θ? That can't be right, do we call the angle θ a different name, like α? Then we'd have θ = α, which seems better. How does this get around the problem?
Things like this don't really confuse me usually, can someone help me out here? Is it bad writing from the author?

Thank you for reading

 

[Hill]

Homework Statement: x
Relevant Equations: x

If I were to ask you, what is the equation of the radial line, what would you say?

I'd say, θ = const.

 

[Orodruin]

Just to add: This is the polar coordinate equivalent of writing the equation for a line parallel to the x-axis in Cartesian coordinates, which is just $y =$ constant.