Solve tan^2 x = 1/3 for pi/2 < x < pi

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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

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