please help. show full working pls.

Solve Tan²(x) = 1/3 for π/2 < x < π
∴ √[Tan²(x)] = 1/3
So Tan(x) = ±√[1/3]
For Tan(x) = √[1/3] or x = ArcTan(√[1/3]) = π/6 ± nπ
or x = ArcTan(√[1/3]) = π/6 ± nπ, where n is a whole number or zero
The only solution to this equation that fits the domain π/2 < x < π is x = 5π/6
ProfRay
∴ √[Tan²(x)] = 1/3
So Tan(x) = ±√[1/3]
For Tan(x) = √[1/3] or x = ArcTan(√[1/3]) = π/6 ± nπ
or x = ArcTan(√[1/3]) = π/6 ± nπ, where n is a whole number or zero
The only solution to this equation that fits the domain π/2 < x < π is x = 5π/6
ProfRay

Since the given is pi/2 < x < pi, that means x is in the second quadrant meaning tan x is negative.
Hence all you have to do is take the square root of tan^2 x:
tan^2 x = 1/3
tan x =  √(1/3) > Again, negative value since its QII
x = arctan √(1/3)
x = 150
Hence all you have to do is take the square root of tan^2 x:
tan^2 x = 1/3
tan x =  √(1/3) > Again, negative value since its QII
x = arctan √(1/3)
x = 150