Practice: find the limit of a hairy expression.

Calculus Level 3

Evaluate the following limit: \[\lim\limits_{x\to0}\dfrac{\sqrt{\displaystyle \cos^2\left(\sec\left(\sqrt{\displaystyle \tan(x^3)}\right)\right)+\sin\left(2\phi x^4\right)+2+\sqrt{3} }}{\cos(x+1)+\sin(1+\ln(x))+\ln(x)}\] where \(\phi=\dfrac{1+\sqrt{5}}{2}\).

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