Let's break this down step by step:

Calculate cos$-2\pi /3$:
cos$-2\pi /3$ = cos$-120°$ = cos$240°$

Using the unit circle, we know that cos$240°$ = -1/2.
Therefore, cos$-2\pi /3$ = -1/2.

Calculate tan$-3\pi /4$:
tan$-3\pi /4$ = tan$-135°$

Using the unit circle, we know that tan$-135°$ = -1.
Therefore, tan$-3\pi /4$ = -1.

Finally, multiply the results:
√3 cos$-2\pi /3$ tan$-3\pi /4$ = √3 $-1/2$ $-1$ = √3/2

Therefore, the final result is √3/2.