Evaluate the expression

tan^5x+tanx+1=0\\ \ tan^5x+tanx+sec^2x-tan^2x=0\\ \ tan^2x(tanx-1)(tan^2x+tanx+1)=-tan^4x(tanx-1)^2(tan^2x+tanx+1)\\ \implies tan^2x(tanx-1)=-1\\
I need tan³x+tan²x+1tan²x

I have tan³x+1=tan²x

Thus reqd ans =2.

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yup right. In fact, you can use the fact that x²+x+1|x⁵+x+1 and obtain the factorisation

tan⁵ x + tan x + 1 = (tan² x + tan x + 1)(tan³x-tan² x + 1) to infer that tan³ x - tan² x +1 = 0.