What's the equation to find theta in an isosceles triangle when you are given all three sides? Theta being the unknown angle joining the adj

If it's a right-angled isosceles triangle the angle is 45°.  If it's a non-right-angled triangle, for which you know all the sides, you can use the cosine rule:  cosA = (b² + c² - a²)/(2*b*c)  where a is the side opposite angle A, and b and c are the other two sides.

If you have a right angled triangle and all 3 sides you can find either of the missing angles using ANY of the inverse trigonometric ratios.