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$$\sin 75^\circ =$$
$$\frac{\sqrt{3} + 1}{\sqrt{3} - 1}$$
$$\frac{\sqrt{3} - 1}{\sqrt{3} + 1}$$
$$\frac{\sqrt{3} - 1}{2\sqrt{2}}$$
$$\frac{\sqrt{3} + 1}{2\sqrt{2}}$$
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