Finding two angles in a triangle when one angle is known

[k_poorahong]

Homework Statement

If we know θ3, A, B, C, How can we find these 2 angle (θ1 and θ2). Please help me find the equation.

Homework Equations

Credit : http://www.mathsisfun.com/algebra/trig-sine-law.html
The Law of Sines (or Sine Rule) is very useful for solving triangles:

It works for any triangle:

a, b and c are sides.

A, B and C are angles.

(Side a faces angle A,
side b faces angle B and
side c faces angle C).

a/sin A = b/sin B = c/sin C

The Attempt at a Solution

 

[Simon Bridge]

Welcome to PF;
You are on to a good start with the law of sines and the law of cosines.
Did you try applying them?

It may help to arm yourself with a list of trig identities too.
Note: you may have to use the unlabelled lengths and angles as intermediate steps.
Don't be frightened to experiment.
For instance - if θ1=θ3, then What is the relationship between B and C?
In this case they are not equal though - what is the relationship?