Is the number satisfying $\eta=\sin(\cos(\eta))$ transcendental?

Question

I was graphing the function $\sin(\cos(\sin(\cos(\sin(\cos...$ when I realized it started to flatten out. This meant that this approaches a constant. Since the sine and cosine repeat, we can make a finite equation for the number that I will call $\eta$: $$\eta=\sin(\cos(\eta))$$Is this transcendental? I know that $\sin$ and $\cos$ are transcendental functions, but I am not sure that the composition of two transcendental functions gives a transcendental number.