Image formed by two plane mirrors inclined at an angle

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How do we calculate the number of images formed by a pair of plane mirrors ? What will be the number of images if not calculated is a fraction? Calculate the number of images formed if the angle between the mirrors is 1 50∘ 2 72∘.

Derive:

Number of images formed by two plane mirrors inclined at an angle of $\theta$ is given by $$\frac{360}{\theta} -1 $$

What I think: Inclined mirror forms images in the circle and one image lies in one sector.

No of images = Number of sectors=$\frac{360}{\theta}$

And $1$ is subtracted from $\frac{360}{\theta}$ because a sector is occupied by the object.

I think this is not a proper derivation. How to prove that Inclined mirror forms images in the circle?

I saw an answer but I didn't understand it.

How to derive it formally?

What's correct:
Let $$n=\dfrac{360}{\theta}$$ where $\theta$ is the angle between the two mirrors

If $n$ is even: $$\mathrm{Number\ of\ images}=n-1$$ If $n$ is odd and the object is placed symmetrically: $$\mathrm{Number\ of\ images}=n-1$$ If $n$ is odd and the object is not placed symmetrically: $$\mathrm{Number\ of\ images}=n$$ If $n$ is in decimal then only integral part is taken and above rules are followed.

It should be noted that above the 'number of images' means the number of images formed.

Experiment work:

$\color{red}{\theta=30^\circ}$

Simulator:

Plus corner: I don't think there exists a derivation to the above formulae. Maybe it was found by experiments.

Note: A very tiny change in the angle can spilt the farthest image.