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
By inspection, $\Theta=0$ is a solution. There's little hope of solving this analytically unless you can find a closed form for the left-hand side for general $\Theta$.

Addendum: $\Theta=\pi$ is another solution because it produces the same RHS as $\Theta=0$, and the LHS $$(-1)^{0^{(-1)^0\cdots}}$$ converges to $1$ (the value of the RHS).
Answer is one $1$ but the answer given by the first vote is wrong because the expansion of (sin2o-1)2 is not equal to cos2o