Here's one way.

Prime factorization of 1763 is 41 * 43.

From Wilson's theorem, 40! is congruent to -1 (mod 41).

We know 42! is congruent to -1 (mod 43). So 42*41*40! is congruent to -1 (mod 43) which is congruent to 42 (mod 43). You can multiply each side by 42^(-1) and get 41*40! is congruent to 1 (mod 43). Then multiply each side by 41^(-1) which you can compute.

Then you can combine with CRT.