<s>[INST] Difficulty in solving challenging trig equation Find $\theta$ on $[0, 2\pi)$ such that
$$\cos{\theta}^{\sin{\theta}^{\cos{\theta}^{\dots}}} = 2 + 2\sec^2{\theta}\tan^2{\theta} - \sec^4{\theta} - \tan^4{\theta}$$
I'm not sure on how to tackle this problem. I've never really dealt with exponentiation of trig functions. Any help is helpful. Thank you very much
 [/INST] $$2 + 2\sec^2{\theta}\tan^2{\theta} - \sec^4{\theta} - \tan^4{\theta}=2+\frac{2*\sin^2\theta}{\cos^4\theta}-\frac{1}{\cos^4\theta}-\frac{\sin^4\theta}{\cos^4\theta}=\frac{2\cos^4\theta-(\sin^4\theta-2\sin^2\theta+1)}{\cos^4\theta}=\frac{2\cos^4\theta-(\sin^2\theta-1)^2}{\cos^4\theta}=\frac{2\cos^4\theta-(\cos^2\theta)^2}{\cos^4\theta}=1$$
So the whole exponent has to be 0 which is easy to tackle with(I guess you don't need help with that)
</s>