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Geometry Level 2

(logcosxsin2x)(logcos2xsinx)=4\large \left( \log_{\cos x} \sin^2 x \right) \left( \log_{\cos^2 x} \sin x \right) = 4

If x=arcsin(y12)+2kπx = \arcsin\left( \dfrac{\sqrt {\color{#D61F06}{y}} - 1}2 \right) + 2k \pi for any integer kk, find y\color{#D61F06}{y}.


Inspired by IME.
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