To solve this equation, we can first simplify it by using the Pythagorean identity for cosine and sine functions:

cos^2$x$ - sin^2$x$ = 1

Now, we can substitute this into the original equation:

cos^2$x$/3 - sin^2$x$/3 = 1

Then, we can multiply the entire equation by 3 to get rid of the fractions:

cos^2$x$ - sin^2$x$ = 3

Now, we can substitute the Pythagorean identity again:

1 - sin^2$x$ - sin^2$x$ = 3

1 - 2sin^2$x$ = 3

-2sin^2$x$ = 2

sin^2$x$ = -1

Since the square of a real number cannot be negative, there are no solutions to this equation.