Here is simple solution: since theta is angle, I am not writing it at the very end. You may assume it.

1 = sin^2 + cost^2,

1/tan^2 = cos^2 / sin^2

1- cos^2 = sin^2

Use these expressions:

sin^2 + cos^2 + (1-cos^2)/tan^2 = 1 + sin^2

Cancel out common parts:

cos^2 - sin^2 * cos^2  / sin^2 = 1

cos^2 - cos^2 = 1

-cos^2 A = sin^2 A

Since there is -ve sign , and SinA and cosA are both squared term, it does not have real solution. It is April Fool problem.