Solve Sin pi/12= 1/4 (√6 - √2)

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Sin pi/12= 1/4 (√6 - √2) ?

I took sin pi/12 = sin (4pi / 12 - 3pi/12) = sin (pi/3 - pi/4)

Did I do this right?
 
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And then used the difference formula? The answer looks ok to me.
 
You can, of course, just put sin(pi/12) into your calculator and check that it matches 1/4 (√6 - √2), if you want to check yourself.