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m = var('m')
#eq=function('eq')(m)
eq = -cos(m)^4*e^(3*m) - 2*cos(m)^2*e^(3*m)*sin(m)^2 - e^(3*m)*sin(m)^4;show(eq);
show(solve(eq==0,m))
show(eq(m=1/2*pi))
−cos⁡(m)4e(3 m)−2 cos⁡(m)2e(3 m)sin⁡(m)2−e(3 m)sin⁡(m)4\displaystyle -\cos\left(m\right)^{4} e^{\left(3 \, m\right)} - 2 \, \cos\left(m\right)^{2} e^{\left(3 \, m\right)} \sin\left(m\right)^{2} - e^{\left(3 \, m\right)} \sin\left(m\right)^{4}
[m=12 π\displaystyle m = \frac{1}{2} \, \pi]
−e(32 π)\displaystyle -e^{\left(\frac{3}{2} \, \pi\right)}
#Clearly m= 1/2 *pi is not a root!