First of all, let's use the haversine package. We will use the inverse haversine function to get a random calculation given a coordinate and a radius.

The inverse haversine function needs a coordinates pair as the starting point of the calculations, a distance representing the radius, and a direction, which can be an Enum (Cardinal points, represented by multiples of Pi) or a float number.

Also, we need to pass an Enum representing the Distance Unit. The valid values are given by the haversine.Unit class:

```
class Unit(Enum):
"""
Enumeration of supported units.
The full list can be checked by iterating over the class; e.g.
the expression `tuple(Unit)`.
"""
KILOMETERS = 'km'
METERS = 'm'
MILES = 'mi'
NAUTICAL_MILES = 'nmi'
FEET = 'ft'
INCHES = 'in'
RADIANS = 'rad'
DEGREES = 'deg'
```

So you may already get what the secret is: we'll select two random numbers, one for distance, and another for direction.

Let's begin:

```
from haversine import inverse_haversine, Unit
def random_coordinates(coords, radius, unit):
"""
args - coords (Tuple: (lat: float, lng: float)), radius (float), unit (haversine.Unit enum)
returns - new_coords (Tuple: (lat: float, lng: float))
"""
# Choosing a random float between 0 and 2π
random_direction = uniform(0.0, pi * 2)
random_distance = uniform(0.0, radius)
new_coords = inverse_haversine(
point=coords,
distance=random_distance,
direction=random_direction,
unit=unit
)
return new_coords
```

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