Help with Energy at inelastic collision

[FLms]

Homework Statement

A particle of mass m₁ and momentum p₁ collides with a particle of mass m₂ at rest. A reaction occurs, as a result giving two new particles, with masses m₃ and m₄, that are emitted at angles
\theta_3 and \theta_4, in relation to the original direction of m₁. Determine the energy Q that has been produced on the reaction in terms of the masses, the angles and p₁.

Homework Equations

Q = T_f - T_i
T = \frac{p^2}{2 m}

The Attempt at a Solution

p_1 = p_3 cos(\theta_3) + p_4 cos(\theta_4)
p_2 = 0 = p_3 sin(\theta_3) - p_4 sin(\theta_3)
Q = T_3 + T_4 - T_1
Q = \frac{{p_3}^2}{2m_3} + \frac{{p_4}^2}{2m_4} - \frac{{p_1}^2}{2m_1}

I'm stuck here.
I suppose I have to, obviously, express both p_3 and p_4 in terms of p_1, but I'm not exactly sure of how to do it. Or maybe I just need some algebraic manipulation to get rid of both p_3 and p_4.

Any help appreciated.

 

[ojs]

That absolutely correct, you need algebraic manipulation to express p_3 and p_4 in terms of p_1, \theta_3 and \theta_4.

 

[Redbelly98]

... and these are the equations you need to manipulate:

p_1 = p_3 cos(\theta_3) + p_4 cos(\theta_4)
0 = p_3 sin(\theta_3) - p_4 sin(\theta_3)