Define angle of friction, angle of repose and obtain the relation for angle of repose (ie., `theta _(g) = tan ^(-1) mu).`

Explanation

### Step-by-Step Solution

1. **Definitions**:
- **Angle of Friction (θ)**: The angle of friction is defined as the angle between the direction of the resultant force of friction and the normal reaction force. It represents the maximum angle at which a body can remain at rest on a surface without sliding.
- **Angle of Repose (θ_r)**: The angle of repose is the minimum angle of inclination of a plane with the horizontal at which a body placed on it just begins to slide down. It is the angle at which the force of static friction is maximized and balances the component of gravitational force acting down the incline.

2. **Understanding Forces**:
- Consider a block of mass \( m \) resting on an inclined plane making an angle \( \theta \) with the horizontal.
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