The sesquisquare aspect (135 degrees) is a major indicator of unbalance in one's life, either by transit, progression or natally. This aspect is also called the sesquare or the older name is sesquiquadrate. It can represent either a physical challenge such as a genetic imbalance causing a birth defect, or a it may represent a poor or untenable choice of behaviors. If we consider an aspect as starting from the ascendant, the indicator of the totality of the physical body, then the sesquisquare drops you off in the middle of the fifth house, past the trine aspect, but not far enough to be readily available to the changeable energy or immediacy of the quincunx.
The sesquisquare often represents behaviors that are strongly stimulated by subconscious longings, or misguided attempts to make life turn out pleasantly by specific actions. The goal is far different from the result, bringing not what the owner intended because the sesquisquare aspect is irritating, uncomfortable, unhappy, maladjusted, or sorrowful in its result.
There is much ignorance of this aspect, and I am at a loss as to why it is not taught early in one's studies. I think it has to do with the unconsciousness of the choices represented by the aspect. To change a sesquisquare behavior requires a breakthrough in consciousness , or an intervention, such as periodically take place under the influence of a transformational transit by quincunx or the planet Uranus, Neptune or Pluto.
The sesquisquare is a trine plus 15 degrees, incorporating an automatic or locked in behavior or energy force with a small shock. The 15 degree aspect must be in the harmonic group that includes the quincunx, and the semi-sextile, both capable of representing upset of expected patterns.
Another way to think of it is a square (90) plus a semi-square (45), symbolizing a determination to go forward into a behavior with a great deal of energy, without a clear understanding of the actual results of the action. This aspect definitely can represent poor choices made by the individual, unusual or faulty genetic structure, or show a potential outcome of trauma. This results in a misalignment of energy patterns, possibly blockages, or increased energy in a direction chosen through habit.
Usually the antidote, if there is one is contained in either the next major aspect, the quincunx, and the awareness of the difficulty of the sesquare is revealed in the aspect in the middle of those two. That aspect is the 144 degree aspect, or biquintile, which has a lot to do with spiritual growth, and that is after all, a mini-enlightenment or "light bulb" like in the comic strips.