Question 989696
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Use the addition formula for sines:


sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y)     (1)


(see for example the lessons &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Compendium-of-Trigonometry-Formulas.lesson>FORMULAS FOR TRIGONOMETRIC FUNCTIONS</A>&nbsp; and &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A>&nbsp; in this site, 

or any systematic textbook in Trigonometry).


Notice that, &nbsp;since &nbsp;sin(x) = {{{1/3}}}, &nbsp;cos(x) = {{{sqrt(1-(1/3)^2)}}} = {{{sqrt(1 - (1/9))}}} = {{{sqrt((8/9))}}} = {{{2/3}}}.{{{sqrt(2)}}}.


Also notice that, &nbsp;since &nbsp;cos(y) = {{{2/5}}}, &nbsp;sin(y) = {{{sqrt(1 - (2/5)^2)}}} = {{{sqrt(1 - (4/25))}}} = {{{sqrt(21/25)}}} = {{{1/5}}}.{{{sqrt(21)}}}. 


Now substitute these expressions into the formula &nbsp;(1).


Good luck.