= sin(-11π/3) cos(13π/4) tan(-5π/6) * cot(7π/6)

First, let's determine the values of sin and cos:

sin(-11π/3) = sin(-3π + π/3) = sin(π/3) = √3/2
cos(13π/4) = cos(3π + π/4) = cos(π/4) = √2/2

Next, let's determine the values of tan and cot:

tan(-5π/6) = tan(-π + π/6) = tan(π/6) = √3/3
cot(7π/6) = cot(3π + π/6) = cot(π/6) = √3

Finally, let's substitute the values:

= (√3/2) (√2/2) (√3/3) (√3)
= (√3 √2 √3 √3) / (2 2 3)
= (3 2 3) / 12
= 18 / 12
= 3/2

Therefore, sin(-11π/3) cos(13π/4) tan(-5π/6) * cot(7π/6) = 3/2.