Trigophobia

Geometry Level 3

tan1(x2+x+1)+cos1(x2+2x+1)=3π2 \large \tan^{-1} (x^2+x+1) + \cos^{-1} (x^2+2x+1) = \frac{3\pi}2

What is the number of real solutions of xx that satisfy the equation above?

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