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Question: tan(4pi/3+5pi/4)

I worked out the format of the tangent sum of two angles, and:

(Tan(4pi/3)+tan(5pi/4) )/(1-tan(4pi/3)tan(5pi/4))

=(sqrt(3)+1)/(1-(sqrt(3)))

That was my answer

Book answer:-sqrt(3)-2

Please tell me what stupid mistake I'm making if you can. I'm probably really embarrassing myself.