Find all real numbers $x$ between 0 and 360 such that $\sqrt{3} \cos 10^\circ = \cos 40^\circ + \sin x^\circ.$  Enter all the solutions, separated by commas.
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Find all real numbers $x$ between 0 and 360 such that $\sqrt{3} \cos 10^\circ = \cos 40^\circ + \sin x^\circ.$  Enter all the solutions, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
70,110
Find all real numbers $x$ between 0 and 360 such that $\sqrt{3} \cos 10^\circ = \cos 40^\circ + \sin x^\circ.$  Enter all the solutions, separated by commas.
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