**Given Expression:**

The given expression is 18sin^2(theta) + 2cosec^2(theta) - 3.

**Simplifying the Expression:**

To find the least value of the expression, we can simplify it and analyze its behavior.

First, let's simplify the expression step by step:

1. Start with the expression 18sin^2(theta) + 2cosec^2(theta) - 3.

2. Rewrite cosec^2(theta) as (1/sin^2(theta)). The expression becomes 18sin^2(theta) + 2(1/sin^2(theta)) - 3.

3. Combine the terms with sin^2(theta) by finding a common denominator. The expression becomes (18sin^4(theta) + 2 - 3sin^2(theta))/sin^2(theta).

4. Simplify the numerator by factoring out sin^2(theta). The expression becomes (sin^2(theta)(18sin^2(theta) - 1) + 2)/sin^2(theta).

5. Cancel out the common factor of sin^2(theta) in the numerator and denominator. The expression becomes 18sin^2(theta) - 1 + 2/sin^2(theta).

**Analyzing the Expression:**

Now that we have simplified the expression, let's analyze its behavior to find the least value.

1. The value of sin^2(theta) ranges from 0 to 1, inclusive. Therefore, the term 18sin^2(theta) will always be non-negative.

2. The term 2/sin^2(theta) will be positive or zero, as sin^2(theta) is always positive.

3. The term -1 is a constant and does not depend on theta.

4. Since 18sin^2(theta) is always non-negative and 2/sin^2(theta) is always positive or zero, the minimum value of the expression occurs when 18sin^2(theta) is minimized.

5. The minimum value of sin^2(theta) is 0, which occurs when theta is a multiple of pi.

6. Substituting sin^2(theta) = 0 into the expression, we get (-1 + 2/0) which is undefined.

**Conclusion:**

Therefore, the given expression does not have a minimum value as it is undefined when sin^2(theta) = 0.