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解：
∵ sina = 15/17,a∈（π/2,π)
∴ cosa = -√(1-sin²a) = -8/17
∴ sin(π/3+a) = sin(π/3)cosa + cos(π/3)sina
= (1/2)√3×(-8/17) + 1/2×15/17
= (15-8√3)/34
sin(π/3-a) = sin(π/3)cosa - cos(π/3)sina
= (1/2)√3×(-8/17) - 1/2×15/17
= -(15+8√3)/34
∵ sina = 15/17,a∈（π/2,π)
∴ cosa = -√(1-sin²a) = -8/17
∴ sin(π/3+a) = sin(π/3)cosa + cos(π/3)sina
= (1/2)√3×(-8/17) + 1/2×15/17
= (15-8√3)/34
sin(π/3-a) = sin(π/3)cosa - cos(π/3)sina
= (1/2)√3×(-8/17) - 1/2×15/17
= -(15+8√3)/34
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