Given:
- ABCD is a square plot.
- The angle of elevation of the top of a pole standing at D from A or C is 30 degrees.
- The angle of elevation of the top of a pole standing at D from B is θ.

To Find:
The value of tan θ.

Solution:

Step 1: Understanding the Problem
We are given a square plot ABCD, and we need to find the value of tan θ, where θ is the angle of elevation of the top of a pole standing at D from point B.

Step 2: Analyzing the Problem
Let's draw a diagram to understand the situation better:

```
A ________ B
| |
| |
| |
D|________|C
```

From the information given, we know that the angle of elevation of the top of the pole from point A or C is 30 degrees. This means that when we draw a line from point A or C to the top of the pole, it will form a 30-degree angle with the ground.

We are also given that the angle of elevation of the top of the pole from point B is θ. Therefore, when we draw a line from point B to the top of the pole, it will form an angle of θ with the ground.

Step 3: Applying Trigonometry
We can use trigonometry to find the value of tan θ. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In our case, let's consider the right triangle formed by the line from point B to the top of the pole and the line connecting point B to point D. The length of the opposite side is the height of the pole, and the length of the adjacent side is the distance between point B and point D.

Let's denote the height of the pole as h and the distance between point B and point D as x.

```
A ________ B
| |
| h |
| |
D|________|C
```

Using the trigonometric definition of the tangent, we have:

tan θ = opposite/adjacent = h/x

Therefore, the value of tan θ is h/x.

Step 4: Applying Geometric Properties
Since ABCD is a square plot, the distance between any two adjacent corners (such as AD, AB, or AC) will be equal.

Let's denote this distance as d.

```
A ________ B
| |
| h |
| |
D|________|C
```

In the triangle ADB, we can use the properties of a right triangle to relate the height of the pole (h) and the distance between point B and point D (x) to the distance between point A and point D (d).

Using the Pythagorean theorem, we have:

d^2 = h^2 + x^2

Since ABCD is a square plot, the distance between point A and point D is equal to the distance between point A and point B, which is equal to d.

Therefore, we can rewrite the equation as:

d^2 = h