You can use the sin angle sum formula:
sin(color(red)A+color(blue)B)=sincolor(red)Acoscolor(blue)B+sincolor(blue)Bcoscolor(red)A
Since 255^@ is the sum of 225^@ and 30^@, we can write:
color(white)=sin(255^@)
=sin(color(red)(225^@)+color(blue)(30^@))
=sin(color(red)(225^@))cos(color(blue)(30^@))+sin(color(blue)(30^@))cos(color(red)(225^@))
Here's a unit circle to remind us of some sin and cos values:
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color(white)=sin(color(red)(225^@))cos(color(blue)(30^@))+sin(color(blue)(30^@))cos(color(red)(225^@))
=color(red)(color(red)-sqrt2/2)*cos(color(blue)(30^@))+sin(color(blue)(30^@))cos(color(red)(225^@))
=color(red)(color(red)-sqrt2/2)*color(blue)(sqrt3/2)+sin(color(blue)(30^@))cos(color(red)(225^@))
=color(red)(color(red)-sqrt2/2)*color(blue)(sqrt3/2)+color(blue)(1/2)*color(red)cos(color(red)(225^@))
=color(red)-color(red)(sqrt2/2)*color(blue)(sqrt3/2)+color(blue)(1/2)*color(red)-color(red)(sqrt2/2)
=color(red)-color(red)(sqrt2/2)*color(blue)(sqrt3/2)color(purple)-(color(blue)1*color(red)sqrt2)/(color(blue)2*color(red)2)
=color(red)-color(red)(sqrt2/2)*color(blue)(sqrt3/2)color(purple)-color(purple)sqrt2/color(purple)4
=color(purple)-(color(red)sqrt2*color(blue)sqrt3)/(color(red)2*color(blue)2)color(purple)-color(purple)sqrt2/color(purple)4
=color(purple)-color(purple)sqrt6/color(purple)4color(purple)-color(purple)sqrt2/color(purple)4
=color(purple)(-sqrt6)/color(purple)4+color(purple)(-sqrt2)/color(purple)4
=color(purple)(-sqrt6-sqrt2)/color(purple)4
This is the result. You can use a calculator to check your work:

Hope this helps!