How can I solve this Trigonometry equation in RxR?

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To solve the trigonometric equations sin(3x) = cos(2y) and sin(x + π/3) = cos(y - π/3) in RxR, one approach is to use trigonometric identities to simplify the equations. The attempt to square both sides and convert to cos(2a) did not yield a valid solution, resulting in y = 0, which was incorrect. Utilizing the sine and cosine addition formulas can help in transforming the second equation for further analysis. This method may lead to a more manageable form to solve for x and y. Exploring these identities is crucial for finding the correct solutions in the given range.
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Homework Statement


we have sin(3x)=cos(2y)
sin(x+pi/3)=cos(y-pi/3)
solve in RxR

Homework Equations





The Attempt at a Solution


i tried squaring both sides and turning everything to cos 2a then turning it into an XY=0
but that didn't help at all i ended up with y=0 which turned out to be wrong
 
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