A geometry problem by Soikat Das

Geometry Level 3

\[\dfrac{\tan x}2 + \left (\dfrac{\tan x}2 \right)^2+ \left (\dfrac{\tan x}2 \right)^3 + \left (\dfrac{\tan x}2 \right)^4 + \cdots = 100 \]

Which of the following values represents the best possible approximation for the root to the equation above?

Clarification: Angles are measured in degrees.

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