一道高中数学题目，求详细的解答过程？

Question

等差数列an中，a2+a6=3π/2，则sin(2a4-π/3)=？

Answer 1

利用等差数列的性质：a2 + a6 = 2a4 = 3π/2，所以 a4 = 3π/4.因此 sin(2a4-π/3) = sin(3π/2-π/3) = sin(7π/6) = -sin(π/6) = -1/2.

Answer 2

利用等差中项性质 2a4=a2+a6=3π/2 sin(2a4-π/3)=sin(3π/2-π/3) 再用诱导公式 =-cosπ/3=-1/2

Answer 3

a2+a6=2a4,sin(2a4-pi/3)=sin(pi/3)=√3/2