A hositive angle less than $$ 720^{\circ} $$ that is coterminal to $$ 204^{\circ} $$ is $$ \square^{\circ} $$.

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To find a positive angle less than $$ 720^{\circ} $$ that is coterminal with $$ 204^{\circ} $$, we can use the concept of coterminal angles. Coterminal angles differ by integer multiples of $$ 360^{\circ} $$.

The general formula for coterminal angles is:
$$
\text{Coterminal Angle} = 204^{\circ} + 360k^{\circ}
$$
where $$ k $$ is any integer.

We need to find the angles that fall within the range $$ 0^{\circ} < \theta < 720^{\circ} $$.

1. **For $$ k = 0 $$**:
   $$
   \theta = 204^{\circ} + 360 \times 0 = 204^{\circ}
   $$
   This angle is positive and less than $$ 720^{\circ} $$.

2. **For $$ k = 1 $$**:
   $$
   \theta = 204^{\circ} + 360 \times 1 = 564^{\circ}
   $$
   This angle is also positive and less than $$ 720^{\circ} $$.

3. **For $$ k = 2 $$**:
   $$
   \theta = 204^{\circ} + 360 \times 2 = 924^{\circ}
   $$
   This angle exceeds $$ 720^{\circ} $$, so it's not within the desired range.

Therefore, there are two possible positive angles less than $$ 720^{\circ} $$ that are coterminal with $$ 204^{\circ} $$:
- $$ 204^{\circ} $$
- $$ 564^{\circ} $$

Given that the question asks for a single angle, the primary coterminal angle within the first $$ 360^{\circ} $$ is typically preferred. However, since the range extends up to $$ 720^{\circ} $$, both $$ 204^{\circ} $$ and $$ 564^{\circ} $$ are valid answers.

**Answer:** $$ 564^{\circ} $$
A positive angle less than $$ 720^{\circ} $$ that is coterminal to $$ 204^{\circ} $$ is $$ 564^{\circ} $$.

A hositive angle less than \( 720^{\circ} \) that is coterminal to \( 204^{\circ} \) is \( \square^{\circ} \).

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