For given values of angular speed and acceleration due to gravity, find the position (latitude) where acceleration due to gravity is
`(a)` Maximum and `(b)` Minimum

Explanation

To find the positions (latitudes) where the acceleration due to gravity is maximum and minimum, we need to analyze the effective gravitational acceleration \( g' \) at different latitudes on Earth, taking into account the Earth's rotation.

### Step-by-Step Solution:

1. **Understanding Effective Gravitational Acceleration**:
The effective gravitational acceleration \( g' \) at a latitude \( \theta \) can be expressed as:
\[
g' = g - \omega^2 r \cos^2 \theta
...