We can simplify this expression by first calculating arccos(3/sqrt(34)), then multiplying the result by 15.

Let x = arccos(3/sqrt(34))

Then cos(x) = 3/sqrt(34)

Squaring both sides, we get cos^2(x) = 9/34

sin^2(x) = 1 - cos^2(x) = 25/34

sin(x) = sqrt(25/34) = 5/sqrt(34)

Now, we know that arccos(x) + arcsin(x) = pi/2, so adding arccos(3/sqrt(34)) + arcsin(5/sqrt(34)) = pi/2

Now we can calculate arctan(5/3), since arctan(x) = arctan(sin(x)/cos(x)), then multiply by 15:

arctan(5/3) ≈ 59.04 degrees

Therefore, 15 * arctan(5/3) ≈ 885.6 degrees.