To calculate sin(25π/3), we need to first determine the reference angle in the interval [0, 2π).

25π/3 = 24π/3 + π/3 = 8π + π/3 = 2π + π/3

This means that the angle is π/3 radians beyond 2π, equivalent to an angle in the first quadrant.

sin(π/3) = sqrt(3)/2

Next, to calculate cos(-17π/2), we have:

-17π/2 = -8π - π/2

Since going π/2 radians to the left of -8π would result in an angle within the first quadrant, the cos of the reference angle is the same as the cos of -8π + π/2.

cos(-8π + π/2) = cos(π/2) = 0

Lastly, to find tan(10π/3), we need to identify the reference angle using the same logic as before:

10π/3 = 9π/3 + π/3 = 3π + π/3 = 2π + 2π/3

This indicates that the angle is 2π/3 radians beyond 2π, in the second quadrant.

tan(2π/3) = -√3

Therefore, the result of the expression sin(25π/3) - cos(-17π/2) - tan(10π/3) would be:

sqrt(3)/2 - 0 - (-√3)
= sqrt(3)/2 + √3
= (sqrt(3) + 2√3)/2
= 3sqrt(3)/2

So the final answer is 3sqrt(3)/2.