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Let sin^-1 (-√3 /2) = x and cos^-1 (-1/2) = y

⇒ sin x = (-√3/ 2) and cos y = -1/2

We know that the range of the principal value branch of sin^-1 is (-π/2, π/2) and cos^-1 is (0, π).

We also know that sin (-π/ 3) = (-√3/ 2) and cos (2π/3) = -1/2

∴ Value of sin^-1 (-√3 /2) + cos^-1 (-1/2) = -π/3 + 2π/3

= π/3