Use properties of determinants to evaluate :
`|{:(102,18,36),(1,3,4),(17,3,6):}|`

Answer

To evaluate the determinant of the matrix

\[ \begin{vmatrix} 102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6 \end{vmatrix} \]

we will use the properties of determinants.

### Step 1: Factor out common elements from the first row
We notice that the first row has a common factor of 102. We can factor this out:

\[ 102 \begin{vmatrix} 1 & \frac{18}{102} & \frac{36}{102} \\ 1 & 3 & 4 \\ 17 & 3 & 6 \end{vmatrix} \]

Calculating the fractions gives us:

\[ 102 \begin{vmatrix} 1 & \frac{1}{5.67} & \frac{1}{2.83} \\ 1 & 3 & 4 \\ 17 & 3 & 6 \end{vmatrix} \]

However, for simplicity, we will keep it as is for now.

### Step 2: Simplify the determinant using row operations
Next, we can use row operations to simplify the determinant. We can subtract the first row from the second row:

\[ \begin{vmatrix} 102 & 18 & 36 \\ 0 & 3 - 18 & 4 - 36 \\ 17 & 3 & 6 \end{vmatrix} \]

This gives us:

\[ \begin{vmatrix} 102 & 18 & 36 \\ 0 & -15 & -32 \\ 17 & 3 & 6 \end{vmatrix} \]

### Step 3: Use properties of determinants
Now, we can evaluate the determinant. Notice that the second row has been simplified, and we can now use the property that if two rows are proportional or identical, the determinant will be zero.

### Step 4: Check for proportional rows
We can see that if we multiply the second row by a scalar, we can find that the first and the third rows are not proportional, but we can check if the second row can be expressed as a combination of the first and third rows.

### Step 5: Calculate the determinant
Now we can calculate the determinant using cofactor expansion along the first row:

\[ = 102 \left( (-15) \cdot 6 - (-32) \cdot 3 \right) \]

Calculating this gives:

\[ = 102 \left( -90 + 96 \right) = 102 \cdot 6 = 612 \]

### Final Step: Conclusion
Thus, the value of the determinant is:

\[ \boxed{0} \]