First, we can rewrite arctan(√3) as π/3 since arctan(√3) is the angle whose tangent is √3.

Therefore, the expression becomes arctan(2+√3) + π/3.

Next, we can use the tangent addition formula: tan(A+B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B)).

Using this formula, we can calculate tan(arctan(2+√3) + π/3):
= (tan(arctan(2+√3)) + tan(π/3)) / (1 - tan(arctan(2+√3))tan(π/3))
= ((2+√3) + √3) / (1 - (2+√3)√3)
= (2+2√3+√3) / (1 - 6 - 3)
= (2+3√3) / (-8)

Finally, we find arctan of this result to get the final answer:
arctan((2+3√3) / (-8)) ≈ -0.651.

Therefore, the final answer is approximately -0.651.