Pre Calculus trigonometry

Question

Solve −2tan(1/2x)+4=6 for 0≤x≤2π.

after solving i got x=3π/2 but I am not sure if it’s correct or not

Answer 1

-2tan(1/2x) = = 2; tan(1/2x) = - 1; 1/2x = - π/4 + nπ; x = - π/2 + 2nπ; n = 1 we have x = 3π/2 only solution

on interval [0, 2π]