help with solid trig problem

I am in ned of help in construction and solving this problem. I am in an independent study program. This triangular pyramid is a type II as the book puts it. 3 faces are right triangles and the 4th in a diagonal plane is an oblique triangle. The book explaines that if the angle to be found is in the oblique triangle you should solve for an auxiliary angle in the third right angle which lies at the same vertex as the required angle, thus spliting the pyramid into 2 parts. I need help constructing the auxiliary angle. The problem is to solve Beta with one face angle at 25 degrees and Theta which is 22 degrees. Thank You

Trigonometric problem

Solve this trigonometric equation for x where 0

Solving for Angle Beta (Trigonometry Problem - Type IV)

In the attached problem I need to solve for the unknown angle Beta. The book calls it a type IV problem and gives the procedure on how to solve for a type IV problem. I have tried to solve this problem but with no luck. I have attached the problem, the procedures to solve for the type IV and the formulas and pictue of a type I figure. I would like to be able to solve this problem the way the book explains.

Trigonometric formulas

Using the exact value cos(pi/4) = 1/square root of 2 and a trigonometric formula, show that sin (pi/8) = (square root of (2 - Square root of 2)/2. Using exact value cos(pi/6) = (square root of 3)/2 and a double angle formula to obtain an expression for the exact value of sin(pi/12)

Solve for beta

In the attached problem, I am trying to solve for Beta. We have done other problems that solve for the faces of the triangle but not sure on how to solve for this face.