Hello David,
If you isolate 1 on the right-hand side you get:
sin2x cos3x + sin3x cos2x = 1
The left-hand side looks like the trig identity sin (A+B). Recall that: sin(A+B) = sinA cosB + sinB cosA.
In this case, A = 2x, B = 3x, so you can rewrite the equation as sin(2x+3x) = 1
sin 5x = 1
5x = π/2, 5π/2, 9π/2, etc. (keep adding/subtracting 2π to find additional answers)
to get x, divide all answers by 5: x = π/10, 5π/10, 9π/10, etc. (keep adding/subtracting 2π/5 to get additional answers)
The smallest positive value of x is π/10, and that is your answer.
