I solved the following equation yesterday for fun and I have the exact result (But these are just some solutions, not all): $$\sin(x)^{\sin(x)}=2 \iff x=\frac{\pi}{2}-i\ln (\exp^{W(\ln(2))}\pm{\sqrt{\exp^{2W(\ln(2))}-1}}) +2k\pi,$$ for $k\in\mathbb{Z}$, where $i$ is the imaginary unit and $W$ is the Lambert $W$ function.
But how can I solve $\sin(x)^{\cos(x)}=2$ now? Thank you for your answers!